The Model 15 is a 38 special revolver....the barrel is marked 357 of course, as it is from a revolver that was originally chambered for both 38 and 357. The barrel doesn't matter, the frame and cylinder of the revolver matter....
Shoot 38's in it to your hearts content. It won't fire 357 rounds, which as you noted are too long for the cylinders. Enjoy it as it with the 38's....