There really is only one real choice. The Ruger LCR.
Its trigger feels like a J frame S&W that has had $300 worth of work done to it. It is simply the most shootable small snub nosed revolver that you can buy. The trigger makes the gun.
Re the 340 PD. I have owned one of these for about 12 years. (I won it at a raffle at the S&W Winter Nationals). It is an amazing piece of engineering. But I almost never shoot it in .357.
I am not recoil shy. I would rather shoot an 8" .500 S&W magnum than the 340 with full boat .357 loads.
Also, if you research muzzle velocity, you would be amazed how low it is for all that flash, bang, and ouch. The tiny barrel really doesn't give most .357 loadings room to get up to speed.
Back when the 340 came out, S&W offered a 342. It was an aluminum frame gun, like the 340 (but without the scandium alloying) and it also had a Ti cylinder with a stainless barrel liner pressed into an aluminum barrel.
It was even lighter than the 340. I believe the 340 is about 12 ounces and the 342 was about 10.5 ounces. Either way, if you want the lightest S&W J frame you can buy, a used 342 is your answer.