My thoughts on worms is that if there are worms in the environment where the local wild animals have them your chickens have already been exposed. I don't see that it makes any difference if you take preventive measures or not.
When I feed anything larger than a mouse to the flock I generally just cut it open and toss it in the run. How long it takes them to finish it will depend on how many chickens you have and how big the critter is to start with. I don't like to leave the dead critter in the run overnight, it can attract predators. I have seen a rooster chase crows away that wanted to help finish it off.
If you are concerned about worms, you can cook the meat first. Since worms live in the digestive tract, you could gut the animal first and not give them the guts. If you wish you can cut the meat into parts and freeze it, feeding it to them gradually. Or eat the parts you want to and toss them the rest of the carcass.
When live-trapping squirrels I've found a very good bait is Boss, Black Oil Sunflour Seeds. I lightly scatter BOSS around the entrance to the trap as well as behind the trip plate in the trap. At the base of a tree is usually a good spot, they like to stay near a tree when they are feeding.
