It should be ok. That is not high velocity ammo. I would not shoot lots and lots in these old guns. I have a few and they do get shot on occasion. Parts are hard to find if something breaks
Factory .38 S&W ammo is lightly loaded just because of all those many thousands of ancient top-break revolvers remaining in firing condition today. Some reloaders (like me) hod-rod the .38 S&W to .38 Special levels, but such loads should never be used in any top-break revolver.