There should be no problems at all shooting .38 +P+ in a 686, .357 Mag ammo is considerably hotter than that. I'd agree with the other posters and advise just shooting .357 Mag ammo instead. That .38 ammo is just for those who are trying to squeeze that last little bit of oomph out of their .38's, and S&W's warning is directed against that sort of thing.
I currently shoot .38's out of my 686 for practice and have .38 +P's loaded for home defense, but not because I can't handle the recoil of the .357 Mag loads, it is more about flash/bang and overpenetration/wall penetration issues (suburbs, close neighbors). I find that .357 Mags are not unpleasant to shoot from my 686 from a recoil standpoint, but they do have noticeable flash and the bang really gets the other shooters attention at the range!