It is a double - of your appearance at the time of casting
Mislead says that
You become invisible at the same time that an illusory double of you appears where you are standing
The question is, what does the double copy, your current appearance (that is, the false form you are projecting with disguise self) or your true form? Mislead doesn't say which "you" the double copies, but the intent of the spell appears to be that it copies your current appearance, regardless whether that is real or disguised. There are two distinct lines of evidence for this:
The spell is intended to, well, mislead
The whole point of the mislead spell is to fool observers into thinking that the illusory double is the actual you, even if they are witnessing you cast the spell. You become invisible at the same time the illusory double appears in your space - for any observers, nothing has happened to you beyond you making a few hand gestures. At least, that is what they would perceive if the double copied your current appearance. If your current appearance was a disguise, and the mislead spell copied your true appearance instead, observers would immediately notice the incongruity. They might think you had changed your appearance (rather than that your disguised self had become invisible and an illusion of your true self had appeared), but they would not be mislead into thinking nothing had happened. The purpose of the spell would be thwarted. In order for mislead to function as intended, it has to copy your current appearance, whether or not that is a disguise.
Spells interact with your appearance unless they say otherwise
This point is even more implicit, but it goes to the nature of how spells work in 5e (spells do only what they say they do). In general, any spell that interacts with creatures by perceiving them, perceives them as they currently appear, unless the spell specifically says it can see their true form.
For example, consider the scrying sensor produced by clairvoyance, where you can see "through the sensor as if you were in its space." Or the arcane eye, which "has normal vision and darkvision out to 30 feet." Or the sensor of the scrying spell, which allows you to "see and hear through the sensor as if you were there." In each of these cases, the scrying spell registers and transmits only the surface appearance of what it perceives. If anything is magically disguised, that fact is not noted by the spell. If you were there, and your normal vision would be fooled, then the image transmitted to you through the sensor will also fool you.
Contrast this with features and items that actually say they see through disguises. A wand of enemy detection, for example, "can sense the presence of hostile creatures that are ethereal, invisible, disguised, or hidden, as well as those in plain sight." The truesight ability of monsters (referenced in the spell true seeing) permits them to "automatically detect visual illusions...and perceive the original form of a shapechanger or a creature that is transformed by magic." If a spell would interact with the true form of a creature under disguise self then it would say so, and we can otherwise assume that it will be interacting with the creature's false appearance.
Thus, when mislead says that it creates an illusory double, we can assume that it creates an illusory double of your current appearance, whether disguised or not. If it was meant to copy your true form, it would need to specifically say that.
Can you change the double's appearance once cast?
So far my answer agrees with the accepted answer, although I have used slightly different reasoning to reach the same conclusion. However, the original question asks something that that answer does not address:
can the caster...use an action to dismiss Disguise Self in order to make their illusory orc double shift into a human, revealing what they really look like...?
The easy answer to this is no. By the previous logic, the function of mislead is to create a duplicate capable of fooling observers. Suddenly changing from one form to another does not enhance its credibility as 'you'.
Further, the spell does not 'track' your appearance after the creation of the double (spells do only what they say they do). If you cast mislead and then take off your hat, your illusory double does not automatically copy that gesture (although since you control its behavior, you could choose to make it do so - whether your true form actually did so or not). In fact, if the illusion tracked your appearance in real time it would vanish immediately after it appeared, since it would have to copy your new appearance - which is invisible! Simply dismissing your disguise self will not change mislead's illusory double, because once created it does not track your appearance.
That was the simple answer. But there is a more difficult issue to contend with. Mislead also says that:
You can use your action to move your illusory double up to twice your speed and make it gesture, speak, and behave in whatever way you choose.
If you you have an illusion that can be made to behave any way you choose, why can't you choose to have it assume another appearance, whether your true form or any other form? Can it "behave" by appearing to cut off its beard? To grow its beard? To grow a foot in height? To turn from orc to human? What are the limits of its 'behavior'?
Illusions are stable unless otherwise noted
One might think of illusion spells as being all mimsy-whimsy pools of amorphous color. But the illusion spells in 5e generally have pretty static forms. So much so that we can make another assumption as a corollary of spells do only what they say they do: illusions, once made, can be changed only to the extent that they say they can be. For example, the spell minor illusion creates the image of an object: for example, "a chair, muddy footprints, or a small chest". The object itself does not change appearance over the duration of the spell. A more powerful spell like major image allows you to change the illusion, but only in a very defined way:
you can use your action to cause the image to move to any other spot within range. As the image changes location, you can alter its appearance so that its movements appear natural for the image. For example, if you create an image of a creature and move it, you can alter the image so that it appears to be walking.
'Altering the appearance' of the major image does not open it up to turning an illusory orc into a human; rather, it only permits that the movements of the illusory creature to appear 'natural'. Within this context, making mislead's illusory double of you 'behave' any way you choose is limited to the 'natural' behavior expected of your (disguised) appearance. Cutting off your false beard, sure. Instantly growing a beard, no - and certainly not changing instantly from an orc to a human. Your DM may need to adjudicate what is 'natural' for your form, but there is a limit to the 'behavior' you can represent.
As further evidence for this, the OP of the question itself cites in a comment the school of illusions feature malleable illusions:
Starting at 6th level, when you cast an illusion spell that has a duration of 1 minute or longer, you can use your action to change the nature of that illusion (using the spell's normal parameters for the illusion), provided that you can see the illusion.
Another corollary of 'spells (and features) do only what they say they do' is that if a specific feature grants the ability to do something, that ability is not generally available. In this case, if wizards of the illusion school gain the ability to change the nature of their illusions at 6th level, that means other casters of illusion spells do not have this ability, since otherwise the feature would be superfluous. A wizard from another school does not have the ability to change the nature of the double in mislead, nor is that ability granted by the spell itself, specifically because an illusionist school wizard does get that ability as a specific feature of their school.
Mislead's illusory double copies your appearance at the time of casting, even if that appearance is a disguise. Once cast, the appearance of the image can only be changed within the range of what might be considered the natural behavior of the form.