Most HPs won't expand from a snub.
That might have been true in 1975, but not anymore. Unless you are shooting a long out of production stash of old Speer JHP loads with the pinhole hollowpoint.
I've been involved with a lot of shooting and ballistic testing of .38 Special ammunition - professionally in LE and also personally after retirement. The various 158 grian SWCHP swaged lead bullet loads are very effective in a 4" barrel, less so in a 2". Plus the recoil is fairly unpleasant. While these can be handloaded to higher levels for excellent perfomance - or you could buy the very energetic 38-44 clone Buffalo Bore +P version - the recoil becomes much higher and you're ability to shoot accurately and repeatedly is negatively affected. I have used such loads in an old-school 2" S&W Model 10, but that revolver weights over twice what a typical 2" S&W J frame or Ruger Little Crappy Revolver does.
A lighter weight bullet is better choice, especially in an airweight snub.
When it was available, the Remington 125 grain BJHP +P was a very good load, hitting over 900 fps, penetrating 13-14" and expanding to nearly .60 calibre. It is still catalogued, but good luck finding it now that Vista ammo monopoly owns them.
The next best and available choice is the Hornady 110 grain FTX +P load. This also hits over 900 fps, penetrates 12-13" and expands to .50 calibre. Recoil is manageable.
The 148 grain wadcutter is an unspectacular load that generally over-penetrates through ballistic media and people (16-24"), does not expand, and at low velocity from a 2" doesn't have much shocking power either. Reloads are more difficult due to the flush seated bullet. While the recoil is moderate in a full-size gun, in an airweight 2" it's noticeable. Much better than carrying a sharp stick, but I don't think that is the best basis of comparison. Also, good luck finding a factory fresh wadcutter load these days. The 158 grain SWC load is more of the same thing, with an extra 4-12" of over-penetration, and more recoil. Again, these loads are obviously lethal, but not the best choice compared to modern loadings.
There are various other respectable loads out there, but they have various drawbacks such as limited availability, heavier recoil, indifferent accuracy and POI, and inconsistent expansion. The Speer 135 GDHP for example falls into this category... it was designed for 4" service revolvers, and the 2" performance is not reliable. The Federal Micro and Deep Shock or whatever marketing hype they are pushing out as flavor of the month don't have a reliable track record. The old Federal 129 grain HS +P is another loser in a 2" barrel. The Winchester 110 grain STHP is generally reliable and consistent, but penetrates 9-12" and you might or might not find that sufficient. The old-school Remington 125 grain JHP +P with lotsa exposed lead is still sold and used to good - sadly, the lots I have seen since the Vista takeover had horrendous QC and poor performance.
Be safe.
