Welcome to the forum.
I wouldn't shoot it the way it is. The 38 S&W is a bigger round than the 38 special. You should be able to change it out, you will need to check head space and barrel gap. if they turn out OK you are in like flint. But you may need to have the barrel cut back, or other problems that may require a smith to do machine work on it. I have 5 - 686's that I can trade cylinders form one to the other with no problem's, took me awhile to get them that way. Good Luck.