After you've thawed the mouse/rat, use tongs/hemostats/forceps/whatever to put it in the snake's cage. Also, shaking the rodent a little bit while still holding him with the tongs will simulate live movement for the snake and thus make him more likely to eat it.

Feeding the snake while he's still in his enclosure usually is the best option as it makes the entire experience less stressful on him (some won't eat if moved to another location to eat) and you. However, you must keep up a regular maintenance and handling schedule. If the only time you open his enclosure is to feed him, that myth about snakes associating you opening the cage with feeding time suddenly isn't a myth anymore.