By RAW, we have only this:
Action: Creating a disguise requires 1d3×10 minutes of work.
Using Alter Self or activating some effect on a magic armor to look different is one thing, to look exactly like someone else is a completely different matter.
When you create an elaborate disguise, such mimicking the appearance of someone, you are not just using those effects to change yourself - you must pay attention to every little detail of that the target's appearance. Using magic improves the quality of the disguise (hence the +10 bonus) but has, per RAW, no effect on the time needed to create one.
A DM can change this to permit faster disguises instead of gaining a bonus to the check, which would make sense since you would be doing things "in a hurry", but you would be entering house-rule territory so you should check with your DM.
Notes on combining Disguise Self with Alter Self
Just some insight that may or may not be your situation.
Keep in mind that Hat of Disguise (disguise self actually) and Alter Self are a fragile combo. A DM can rule that since the nature of those spells are different (an Illusion and a Transmutation), those bonus won't stack. You are not effectively creating a better disguise, since anything that you create with Disguise Self (the effect of the Hat of Disguise) will appear "outside" the Alter Self transmutation, and so the Alter Self / Polymorph won't have any real utility. Disguise Self is an Illusion that makes the caster appear as something else, while Alter Self changes the caster per se. For example:
Let´s suppose that Rufus The Lumberjack Wizard used Disguise Self to look like someone. This spell will create an illusion that he is someone else, but it is just that - an illusion.
Then, he uses Alter Self to assume the form of a humanoid that has slimy skin. He will look like the disguise that he created for himself using Disguise Self for everybody. But, if someone touches him, he will feel slimy. Disguise Self is like putting on a mask while Alter Self is more like Plastic Surgery. Even if you take on a face lift and change your face completely, your mask is still the same and the face lift will make no difference when you put your mask on.
In a way, Disguise self creates a "disguise bubble" that makes you appear different, and just that. On my rulings, you won't get the +20 from using both spells, just a +10 (since the effects overlap), when using both to create a complete disguise.
Of course, if you use the "Disguise Self" aspect of the Hat of Disguise to just change the appearance of the armor and clothes, that's a different case, and I suppose that the +20 bonus would be valid and legal, since is like an extra "tool" in your arsenal - one that Alter Self can't emulate, since it can't change gear.