Just to say I would be meshing the hamster cage to stop any further visitations from the mice, as long as they have access to a source of food (the hamsters food bowl) they will keep coming back. Male mice especially can be very territorial and could cause a hamster serious harm. I would also go down the humane trap route but if they have no access to a food source they should move on anyway, if you do manage to catch one you will have to take it for a car journey to release it as they can find their way back over a surprisingly long distance. Meshing cages is very simple btw, I use this for my mice cages
Mesh Panel - Wire Fencing - Gates & Metal Fencing -Gardens - Wickes and fasten it with cable ties, it doenst look stunning but it will stop them getting in. I was trying to find a pic of the hamster heaven I did but I can only find one of the big mouse cage when Id just meshed it, it gives you an idea though.
