If the firearm can use .38 special rounds this ammo can be used on it.
The S&W revolver in question is very old, according to the person asking about ammunition safety, the .38 Special ammo available at that time is the only truly safe ammunition to be used because it is the only available for test firing. I don't know but I doubt if there were any means for pressure testing a revolver cylinder and barrel. I've seen warnings on ammo boxes and revolver data that says only use ammo that it was designed for. Some new revolvers now do not have a +P rating. I don't think the +P ammo is safe to be used in this revolver.
Make sure any firearm you fire +P ammo is rated to fire the extra-powered shell. Not all .38 Special handguns are rated for =P ammo, especially older revolvers. I agree with Zane.