OfftopicOff-topic regarding the shutter.
My main concern would not be the shutter, but:
That you have a good mechanical lens, that do not go crazy changing zoom and auto focusing. Probably a fixed focal prime lens, lets say 85mm.
Discard thoosethose cameras that hide the lens each time you turn them off.
Aim for a 10 Mpx camera so your images are ready for a 4K resolution.
Look for one that can be trigeredtriggered remotely.
USB conectionconnection so you save the images directly to your computer.
Full manual mode, so you have uniform lighting conditions, at least from the camera side. This will probably discard most of small video cameras.
You could use Live view, so you avoid the mirror shaking. This wilwill drain your baterybattery, so take that in mind.
The electronic shutter... I would not want to be limited by this if it compromises any of the above. Look for a camera that has a good warrantee.
And there are afordableaffordable dslr cameras on your price range.