As someone noted there are name catchers who didn't catch until college. Bob Boone was an All American third baseman at Stanford. The Phillies made him a catcher in the minors. Blake Swihart was drafted for his athleticism and moved to catcher in the minors.
I've seen a few middle infielders and centerfielders moved to catcher in high school. They have the hands and the arm.
Pitching and catching? Not a good idea for the arm or the legs.
RJM, the OP said there were 5 catchers and his kid was on the small side. You and the other posters are talking about turning a highly athletic player into a catcher....I think that's a bit different than picking up the gear in 8th grade and beating out 5 guys for the job while trying to pitch.