There's really no need to machine the caps. I just bought some cheap nuts and double nutted the studs. There's enough thread to catch a second nut and they don't need to be torqued down since the cap works as a retainer to keep all the nuts from backing out. I did this and really like the full sized cap on the chrome hummer rims. At least try it on one wheel before cutting your caps. You can use the nuts from another wheel to see if you like the look.
Also, be sure to tell your machinist how big to open. If you just tell him to mill that lip off the inside of the rim, that won't be enough and you will be back to where you started.
My machine shop didn't need to unmount the tires. He just aired them down so he could clamp the rim edge in contact with his milling bench. After milling, they were aired back up. That keeps the tires and rims with a factory balance from GM and saves some more money.