.357 mag IS NOT a PB let me repeat is NOT a PB calibre! While you are correct that a .357 can chamber and fire a .38 Special cartridge, that is not relevant legally as the PB calibre classification for .38 is .38 S&W revolver cartridge and NOT .38 Special.
Though, (due to ignorance on their part) you will be hard pressed to have any licensing authority issue you a NPB license for any .38 revolver...
Also, the service revolvers are chambered for .38 S&W and NOT .38 Special, hence the former being classified as PB and the latter being NPB. The Arms Act is quite specific as to PB calibres being those that are in use with the security forces (Military/ Police etc.).
.357 mag handguns should be entered on a regular NPB pistol/ revolver license, and this rule is applicable uniformly ACROSS INDIA. The Arms Act is not state specific, it is uniform for all states, except maybe for J&K, which IIRC has it's own special laws regarding many things... not sure on the specifics for J&K so cannot comment in detail. If the licensing authority makes a fuss about entering the .357 mag on your NPB license, I would advise you to seek the services of a lawyer and show them the error of their ways!
For several years, one of my cousin's owned a S&W large frame revolver in this chambering - and even that large sized handgun (with all it's added heft) was no pussycat to shoot!

So I can only imagine the kind of blast and recoil on the snub nosed version!
IIRC ammunition was available (though not widely) but expensive. Which is why he sold that in favour of a Beretta pistol in .32 cal.
HTH
Cheers!
Abhijeet