I think that the round nose lead bullets would be O.K.
Modern conventional wisdom is that if a bullet don'e expand, it aint any good. I don't know if that is true or not.
.38 special ammo is not the fastest round in the world, but the 158 grain load is heavy, and the round nose means it will probably penetrate fairly well. Personally, I used to carry LSWCHP in my snubby .38, but the round nose lead would probably have the same result cause the hollow points don't usually expand out of the snubbies anyway.
Just like the story of the polar bear, if that cop had hollow point ammo, and it had expanded, it might not have penetrated deep enough to kill the bear. Same thing with 9mm, ball ammo killed bunches of people during WW2 with no problem. It wasn't untill everyone started loading them with rapidly expanding HP ammo that it was found that it doesn't always penetrate deep enough. You have to balance penetration and expansion / deformation of the round. I think HP's are over rated in handgun ammo.