Can't comment on the 337 Airlite as I have never owned or fired one.
I can offer an opinion on the model 342 pd. Own one in black, fitted with Trijicon nightsights and had an action job done. I would suggest you rent or borrow one if possible before purchasing it. Recoil can be an issue. A gun of such low weight, coupled with a short barrel, definitely "kicks" when fired. I find the recoil acceptable/tolerable, but know others who can't stand it. It isn't the most pleasant gun to shoot in the recoil department. Played around with different grips -- Pachmayr and Hogue, and finally decided to reinstall the standard Uncle Mike grips the gun came with. Overall, since low weight and wheelgun reliability were my most important considerations before buying this gun, I have been happy with it.
If weight isn't a highly significant issue, you might consider a model 640. I have one with a front night sight and installed a Hogue grip. Bought it used, as it was an unsold model that had been used a few times at the firing range my local dealer has. In comparison with the model 342, it is definitely a pleasure to shoot. However, it weighs around 25 ounces, versus the 11 ounce weight of the model 342 pd. Also, it has the ability to handle 357 magnum cartridges, a plus IMO, even though they are mini flame throwers in such a short barrelled revolver.
Try to shoot whatever you wind up buying before purchase. There's often a big difference between how a gun feels when held unloaded in the showroom and how they feel when being shot.
Good luck on your search.