What a coincidence.... Actually, just finished up installing two new tires on a couple of those two-piece wheels (lock ring type - not RH-5) yesterday.
When inflating that type of wheel, I use a clip-on chuck, and a remote valve & gauge. I install the wheel to be inflated on the truck, with the ring facing inward - toward the inner wheel. Inflate in 10 psi increments, with a release to zero in between - just to make sure the tube settles in. Check for proper ring seating using an inspection mirror.
If the ring were to come off, it is trapped between the two wheels, but I still stand back 25 or 30 feet just in case. (Note: The tire being inflated in the attached pic is the one on the truck, NOT the one laying on the floor.)