Ouch!
My Walther PPK in .380 has a fair amount of recoil with standard loads.
With my handloads that push an 88 gr. bullet at 1,000 fps, it's quite a handful.
The ultralite .357 Magnum snubnoses are popular, but talk to the people who shoot them and they're almost always carrying .38 Special loads.
Firing a .357 Magnum in such a light gun is disconcertingly painful.
I'm not one of those who subscribes to the idea that you won't notice recoil in a gunfight. As you train, so shall you react.
If you're flinching while practicing, you'll almost certainly flinch in a real situation -- and you may miss your target.
Frankly, I think ultralite guns are a bad idea. Even in .380 it could be quite a handful, promoting flinching.