I wouldn't use it with full .357 loads. I would instead use well known .357 "lite" loads like Golden Saber or just drop down to some good .38 +P. If you can find a grip that fits your hand right then the recoil can be more distributed through your hand than thrust into a single area of it. It's bulky but the Pachmayr Compac helps me shoot .357's from my 640 and it's stainless steel. I have noticed in a few threads that the 3xx series J frames have a lot of grip frame area deviation more so than any other. I think the sights and the markings are about the only real differences in yours vs. the M&P model. If you don't ask it to be all things in one gun then I bet you will like it. You might buy some wadcutter or other standard pressure .38 to start with and work up to what you can top out with ability to take recoil, still hit your target, and still have use of your hand...
2nd on the Golden Sabers....get your practice with 38 special wadcutters and finish your session with 5-10 magnum rounds. You have found one of the easiest guns to carry, and it has the ability to put forth some very impressive firepower.
The Remington-UMC 125 gr .357 mag rounds have lighter recoil too. I get them from Walmart. I would NOT recommend this stuff as self-defense ammo due to frequently low quality control standards by Rem-UMC. In my lightweight revolvers I usually stick to .38 Spl+P for carry unless I want to impress my friends and family at the range with the really hot stuff. With full-bore top quality .357 mag ammo you will have an experience that you won't soon forget. Maybe someone will chime in here to correct me but as I recall Speer makes a 135 gr Gold Dot .38 Spl+P loading especially for short barrels.
I had a M&P 360 that I eventually sold. I really liked the sights but had trouble shooting it as well as my 442, and a .357 is just too much (for me)in a gun this small.
They are nice carry guns and S&W is still selling lots of them so best of ouck w/yours.