Door latches can cause issues with mice aswell. What I do is, I cut out a strip of plastic from an old ice cream tub, margarine tub or similar ( about two/three inches square). Cut or melt a `slit` in this where the door latch would fit through. Once the slit is made, place this over the door latch and the plastic then lies flat against the cage door and blocks the hole!
Because it`s flat and secured through the metal latch by the slit you have made, the hamster or mouse can`t chew it. You just have to make sure when you open and close your cage door that the plastic is flat and secure and not slack. You can actually melt a few holes in each of the corners of the piece of plastic and use thin cable ties to tie it into the door bars to secure it well so that it does`nt move.