There is nothing wrong with 38 Special
My first pistol I owned while in the USAF was a Model 19 S&W in 357 mag. I sure was alot more fun shooting 38 Specials in it. I found one of my co-workers who reloaded ammo. He later reloaded my 357 brass to 38 special velocities. I would bet your Model 10 has a very sweet single action letoff.