Which is a 1:1 barrel swap in the majority of handguns ( P229, MP40, G22 etc), take a look at the Armorer's manual:
https://static1.squarespace.com/stat...C9+English.pdf
Glock fortay mags feed the sig so thats not an issue. 3 screws and a barrel nut, barrel is a pencil profile w/ a shoulder. Find a gunsmith that's worked with blowback FA SMG's in the past & cuts barrels. .357 case is .37mm longer than a 40, OAL difference is +.16mm for the .357. Probably looking at $5-800 for the barrel work, and 2-4 hours shop time and a few boxes to tune it if you're run up against tolerance stacking. For reference I've seen custom profile 16"-20" rifle barrels quoted around $900 from the likes of Lothar Walther.