Pretty country and a nice, short day hike.
Nice M637, and an old-school +P load. Might not significantly deform or expand, but it has the weight and, normally, sufficient 'reach'.
While I've formerly carried all manner of pistols and revolvers for backwoods activities, nowadays I find my +P capable or .357MAG J's to be suitable choices. The largest threats in the mountains might be a mountain lion, or feral humans.
While I still have a respectable amount of 158gr LSWCHP +P left over from previous years when I favored the load (Rem, W-W & Fed versions), I've come to favor the more modern middleweight +P loads after seeing their performance in organic gel and hearing reports of their successful use in LE hands (meaning for off-duty and Secondary weapons nowadays).
There are some .357MAG loads that produce some surprisingly decent velocities, even from the short barrels, but the average shooter has to ask themselves if the juice if worth the squeeze when it comes to felt recoil and controllability, especially in rapid shot strings. When I do carry a MAG load in one of my M&P 340's, it's typically the mid-range 145gr STHP. Less wrist torque effect than the 125gr loads, and the mid-range STHP has gained an enviable reputation in actual use over the many years of its production.
Anyway, congrats on an enviable day hike in some beautiful country. The 637 is a handy Airweight that's easy to carry.