Sound effects for movies is it's own specialty in Hollywood.
Punches, gunshots, explosions... all of those recorded in real time sound wimpy and actually pretty lame.
The artists who work that specialty are geniuses at creating sounds...... I saw one team of ladies who worked in martial arts films doing the FX.... also... have a look back at some of the radio shows they used to do live on the radio....back in the 30's and 40's..... quite innovative because they also did all their sound FX live.
I would try placing something.... maybe a damp (not wet) paper towel rolled up to simulate a mouse in the trap... that would take the sound of the spring hitting wood away a bit and perhaps that will sound more realistic. You still get the snap, but not as bright and "empty" sounding.
good luck.