Granted, there are better choices for longer barrels ie four inches and above, but many hollow points fail at snub velocities (denim and gelatin tests) unless you want to go +P, and even there, things are problematic. I also heard stories where the 200 gr old Super Police load was the preferred choice in snub noses. I understand that 158 gr RNLs also have a tendency to tumble in the snub nose revolver...I’ve seen tests to that degree.
One should feel adequately protected by a snub nose revolver loaded with the 158 gr RNL particularly when the shooter is skilled in placing their shots accurately. There is no substitute for good marksmanship.
San Antonio police used that 200 grain load. Officer Tom Ferguson was also a gun writer and I met him at an NRA Convention there. He told me that it was a miserable load, even from four-inch barrels and performed poorly when they had to shoot dogs.
If one can't or won't use Plus P, the .38 is a frail reed on which to lean.That 's why I suggested the full power wadcutter round.
Massad Ayoob (I think it was him) has published that SWC bullets don't seem to work a lot better, if any, than RNL ammo.
But many who shoot small game say they do fare better.
Of course, it's a far cry from shooting rabbits or grouse to shooting men or bears. Still, I'd rather have a hard cast SWC at good velocity over a RNL if I had to head shoot a big cat or a bear.
I have Marshall & Sanow's book on handgun stopping power and feel it's realistic in the results described, which in some tables came from real shootings, not from gelatin tests.
The man I know who has shot more men with handguns than anyone else I know of says that well placed 9mm ball ammo fares better than most predict. This was confirmed by the late David W. Arnold. Before migrating from South Africa to the USA, David had been a high police official in Rhodesia. He had access to after action reports and said that 9mm usually worked pretty well on terrorists. But I think he saw more hits from SMG's than from the Walther P-38's his men carried. He wore a P-38 because it was issued. In private life, he preferred the Colt .45 auto and was a member of the Rhodesian international action shooting team. David was a wise man and his preference for the .45 speaks volumes.
Ayoob's tests on slaughterhouse pigs showed good results with the old FBI load of a Plus P LSWCHP. That was far superior to the .380 in those trials. But the OP wants to avoid Plus P ammo. And in his Airweight gun, that's probably wise.