If it were only that easy.
A 9mm barrel won't work. Wrong diameter for the slide -- it'll slop around -- headspace will be wrong, the extractor won't work, the breechface might now be right, etc.
The folks who make it work use a special Bar-Sto conversion barrel designed to work in the .40 gun. It will work with the existing slide, breech face and extractor, and will headspace properly. Visit the SIG Forum if you'd like more info.
It may be that other barrel makers also make similar conversion barrels.