TimBII said it in his comment, but I'll go ahead and make it an answer:
If you turn a sentient biological creature into programmable matter, you're not going to have a sentient biological creature anymore. Even assuming you could "prime" the user's atomic/molecular structure to become programmable matter at the push of a button without yet doing so, when you push that button, the user will cease to exist.
I should also point out that if you can transform normal organic molecules into programmable matter, you don't really need to - you can just rearrange the user's molecules directly. Of course, in so doing, you will kill them, but Star Trek is alright with that.
So, you could have your shape-shifting watch. It transforms the user's matter into some other form which is not the user for a given duration, then restores the user's matter into its previous state. The user will not be conscious (and will in fact, be dead) for the duration of this transformation, but it's a very effective disguise.
Your power source, as was also commented upon, is implausible, but as long as you're not too tied to reality, you can hand-wave the energy requirements with zero-point energy or something similar.
The remaining problem would be the ethical and philosophical conundra that this would create. Did the user die, or simply briefly cease to exist and then resume existing? Are souls real, and do they stick around when the user is not themselves? If your watch can record your complete state right before it transforms you, can that be duplicated on another piece of appropriate-mass matter? If so, is that new construct also you?
These are all interesting things to consider, but you won't have a conscious-in-another-form shapeshifter as a result of your watch.
Edit: There are also enormous problems with both "scanning" the target matter (ie. your user) to a level of definition that includes whatever states are relevant to allow you to reconstruct them after the fact, and rearranging their matter in a rapid fashion that isn't horrifically destructive to everything in their vicinity. But again, we let Star Trek get away with it.