They will work fine. Also in a .38 Special revovler.
For kicks, the .38 Short Colt in a .357 Magnum single action is about like shooting .22 Shorts.
I once shot a .38 Short Colt round into a pond. I could have made a bigger splash if I had thrown the round into the water.
P.S. Though you are not likely to find them, the .38 Colt New Police round will not chamber in the .38 Special/.357 Magnum revovlers. It will fire only in .38 S&W revovlers.