In the past, I have freed sodapop-stuck buttons on remote controls by putting some isopropyl alcohol on the button (letting it run into the nooks and crannies) and then pressing and releasing the button a bunch of times as it dried. (With the device turned off and/or its batteries removed).

Obviously for a camera, you'd want to make sure that the stuff doesn't get into any optical components.

Sometimes I had to do the procedure more than once, as the button got sticky again after it dried. But eventually it freed up after enough repeats.