Am assuming that the desire to use a .22 shot cartridge for trapped animals is to reduce pelt damage. This would probably work at very close range but may not reduce damage as much as desired and at very close range may result in more damage.

In the 1950s I was given two boxes of CIL shot cartridges and used them in my Cooey repeater. Killed a few starlings with them. Between 10 - 15 feet the pattern was a donut of about 25 to 30 inches in diameter. Pellets were in a band about 2 inches wide. On crossing shots one aimed at the bird without leading and many times the starling fell. After every shot, the case failed to extract and had to be pushed out with cleaning rod as the metal crimp was caught in the start of the rifling.

Later, had the use of a smoothbore Remington pump that worked well and was very effective to about 10 feet using head shots on pigeons in the barn without damaging the building. Patterns and killing energy were inconsistent at greater distances.