Personally I find little to no difference in recoil between 40S&W and 357Sig.
This may be true in full size guns. In my experience shooting 9mm, .40 S&W and .357 Sig in the original Keltec P11 series pistols with short barrels and light weight, there was a lot of difference.
I know a Keltec is not a Shield, but some principles transfer directly.
Or, shoot .357 mag through a 2" snub gun. It's like holding a grenade when it goes off. There are intelligent limits to souping up handgun cartridge terminal performance that sometimes even manufacturers mistakenly exceed.
Short barrels do not allow for complete burning of the powder of higher pressure cartridges. They are designed for barrels of at least 4" and preferably longer, and almost always tested for velocity and pressure in 5" barrels.
Max SAAMI pressure for the .357 Sig round is
40,000 psi. When using the European CIP method of measurement, it is 44,240 psi.
Max SAAMI for standard 9mm is 35,000 psi.; +P = 38,500; NATO = 36,500.
Max SAAMI for .40 S&W is also 35,000 psi.
The effects of pressure are not a linear increase, I do not believe. Thus, the 5,000 psi higher rating of the .357 Sig will beat up a gun much more than .40 or +P 9mm.
When .357 Sig is shot from a short 3.1" Shield barrel, it will create a large blast, increased muzzle flip, much louder report and more felt recoil. The ammunition is limited in loadings and manufacturers, and expensive because it is a boutique (low volume) cartridge. The short Shield barrel does not give the cartridge the time/length to get up to velocities that are much more effective than 9mm or .40.
I see no advantage whatsoever in trying to put a .357 Sig barrel in a subcompact handgun, especially the Shield. S&W would offer it if it was marketable, economical, reliable and safe. Pistols that break because of using over-pressure rounds for which they are not designed are not safe, or at least not reliable for self defense purpose because they will barf when not expected, IMO. One does not "need" the .357 Sig cartridge to maximize the effectiveness of a Shield. In truth, it will
decrease the effectiveness of the gun.
Barrel makers know this so they do not bother to offer such barrels. Sure they would custom manufacture a one-off .357 Sig barrel for you, probably with a bunch of disclaimers, and it would set you back far more than the cost of the non-discounted gun. Shops did this back in the 90's when the cartridge was new and people were still learning its limitations. They are much better known now.
Some of this applies to .357 Sig in a full size handgun, but on a reduced scale. In a Glock 35 with an aftermarket extended (Possibly threaded) .357 Sig 6" barrel, it makes sense.
However, please do whatever you
want, but be sure to base your decision on good information. See if you can find anyone with a .357 Sig Shield (you probably can't) and shoot a box of 50 through it. Then decide.