As stated by others, best to pick up a 9mm Tanfo barrel and rechamber. As far as the .357 SIG not having advantages over the .40 , I strongly disagree. I have run .357 SIG in a number of SIG Classic platforms for the past 6 years. Not only are the terminal ballistics better than the .40, it has more accurate, has less muzzle flip, and flatter trajectory. In fact, I have rid myself of every .40 barrel that I have. I also EDC the .357 SIG, something I would not do with the .40 .
I am about to do the same conversion with my Witness Classic, though I have yet to decide if I am going with .357 SIG or 9X25 Dillon. I have reamers and headspace gauges for both... so I will probably try .357 SIG first and see how the pistol likes it.