Quoting a similar response for Charm Person:
"Under Spellcasting…Targets, the PHB states that spells with subtle effects can be cast without being noticed:
Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless the spell says otherwise.
(PH, p 204, emphasis added)
Even the target typically doesn't know
The casting of charm person is subtle enough that even the target doesn't know about the spell until it expires.
When the spell ends,the creature knows it was charmed by you (Charm Person, PH 221)
If even the target of the spell is unlikely perceive it was cast, other observers would have less of a chance. (A court magician, trained in Arcana and watching for such things, would be a different "
That being established, (thank you for the foot work Tim Grant) I would look at what could be considered a "subtle" spell.
It would be up to your DM to decide how subtly Mage Hand can be cast, assuming that a low level spell would be easier to cast/require less movements than a higher level spell with more obvious effects such as fireball.
Personally i would argue that a Sleight of Hand vs Passive/Active Perception based on the scenario would be the way to play it. I feel that Mage Hand, as a cantrip, and using those cited references, would qualify as being a much more subtle spell. Without being able to cast it undetected it greatly limits the usage of Mage Hand Legerdemain to the point of "why even take it".