We went through almost the same thing with my 2017 when he was an incoming Freshman. He was an OF/P with a strong arm and then the Varsity coach saw his Freshman team with two poor catching options and suggested to my son he would have a better chance of playing more as a C (he had caught some in Pony but it had been two years). So what I did was make a deal with him that we would buy some basic used catcher's gear for his Freshman season, and if he still wanted to catch and the coach wanted him too after that season, we'd get better equipment. He was also a good pitcher but the coach resisted using him much that season as a Pitcher because he really needed him as a catcher and the team had good pitching options.
Flash forward to his Soph and Junior seasons and he has been exclusively a Catcher for his HS team. But on his Summer and Fall travel teams he does both. The travel coach knows never to have him do both in the same day. Knock on wood but he has not had any arm troubles. He is aware of the different throwing mechanics and stays within himself pretty well. But I will add that every chance we get to send him to a Catcher's camp he has gone to learn the position. I never knew how hard it was until I watch these camps and see all of the techniques taught. You cannot just become a strong catcher defensively--it takes a lot of work and bruises to get there. Being quick and athletic is a key now to catching--the old model of the heavy set catcher is dying.
For us we have no idea if the dual option of a Catcher/RHP will be attractive to colleges. He is attending several camps and showcases this Summer and hopes to be able to show off both. I hear the people who are saying at some point he will have to choose one, but for now, the option of both may interest a school short of open positions to offer and needing flexibility. I remember what the Stanford coach said at their Pitcher/Catcher camp, and he told him do not give up on one of them until you have to--the more options you present to a college, the better your chances.
So I would say give it a try for a year and see what happens. It might wind up being the best baseball decision he ever made.