Yep, you can size them first in the carbide .40 S&W/10mm die, then in the 357 Sig steel die. I use the Dillon carbide 357 Sig die myself, but there's no need to go to the expense of that die if you already have the .40/10mm die set.
I used to spray a little lube on the brass and just size in my Redding 357 Sig die, then tumble for about 20 minutes in plain corn cob to remove the lube. It's really no big thing, and since I clean the primer pockets on everything I load anyway, that removed any media still in the primer pockets.
If you want to shoot me a PM with any questions, feel free.
Hope this helps.
Fred