HAve had a 'possum problem before. Airguns are one good solution, but do be careful in your selection as many are pretty loud. In gneneral, the pre-charged pneumatics are (1) expensive and (2) loud unless supressed.
Same with the old multi-pump pneumatics. Get good power, but they tend to have a louder "crack" than spring-piston airguns. Can say much the same for CO2 guns, the few that have the power level needed.
Spring-air might be the way to go...and in a larger caliber (.22....there are some .25's).
Neighbor had a possum in his attic...refused traps. I wated up for that critter in a home-made blind on an overlooking roof and nailed it to the ground with a bolt from a crossbow. Needed to be quiet and the crossbow from a sharp downward angle (that's why I was on the roof) had limited chance of skipping off into the neighbors bedroom window.