Regular .40 S&W shoots just fine from a stock G20 with a stock 10mm mag -I do it often, and even reload some 40's for this purpose to shoot from my G20.
.357 SIG is a necked down .40 case. They fit just fine in a stock G20 magazine.
All you need is a .357 SIG barrel, available from Barsto, Jarvis, KKM.
KKM drops right in, without any fitting involved. Barsto or Jarvis might require shipping the gun to the factory for some adjustment.