I *think* you will be OK, because SIG-Sauer makes the P229 in 9mm so you will be shooting it in a caliber the gun is regularly available in.
However, there was a guy with a Glock 31 .357 who wanted to put in a .40 barrel and IDPA HQ told him no, the G31 is not available in .40 so he could not change the caliber and still shoot in SSP. This even though the only difference between a G31 and a G22 is the barrel and the model number marking.
So I would not noise it around too much. If anybody asks, you are shooting a P229 9mm and that is that.
John, some guns like SIG Sauers and Glocks have enough extractor depth and travel to pull a 9mm in a .40 breechface. Usually. The barrelmakers caution that the conversion barrels are for range use only, not duty or defense.