Curious how much of a PITA it would be to convert a 4006 to 357 Sig? I know it won't be a drop in barrel/spring swap like my 229, but...
Anyway, curious for purely hypothetical reasons before I pick up a project.

You'd need a .357 SIG barrel. S&W never made Third Generations in this cartridge (to the best of my knowledge). Bar-Sto, a noted manufacturer of aftermarket barrels, doesn't show anything for Third Generations, only the M&P.

There's a factory 3rd Gen unicorn or two out there, I believe a member of this board posted one not too long ago. Or maybe over on the S&W forum... I wonder if a 3rd Gen 59/69XX 9mm bbl could be re-chambered to the SIG cartridge and then fit to the 40 cal 4006? Gotta be surplus 9mm bbls available out there.
And here is an article showing just what you are looking for. Probably no chance, but might be worth a phone call to BarSto.
Handloader Mag 357 SIG

When I bought my first 4006 in 2008 Bar-Sto had a conversion barrel listed on their web site. Almost bought one but decided against it. I don't see it listed any more.

Here's a thread about an S&W conversion barrel which may be helpful: S&W 3rd Gen Barrels

I have been told the 59 series 9mm barrels have a different outside dimension on the muzzle end and would not fit the 4006 slide. I have not confirmed this for myself.