Having tried the humane traps in our experience they never work. Even if you take them a distance more always move back in.
Having experienced what mice will eat, having all our electics go out only to discover that mice had chewed through the mains cable which was short circuiting into a wooden beam which was scorched and ready to catch fire I cannot tolerate them. Both mice and hamsters, humans, dogs and cats could well have gone up in flames that day
Be aware that also anything that has been in contact with mouse urine or faeces such as bedding, food tins etc can be a source of infection which could spread to your hamsters and yourself.