Hello Evan,
I strongly suggest that you NOT put radial tires on stock Studebaker rims. They were not designed for the stresses radial tires will impose on them. Wheel failure is a definite possibility. This has been discussed in Turnings Wheels. We, too, have a '54 Commander Starliner and I bought a set of wheels from Bob Helm who advertises in Turning Wheels for the P195/75R15 Coker wide whitewall radials that we have. We have no clearance problems with them, and they are very close to the same diameter as the olde bias ply tires so from a few feet away, they have the same appearance.
Yes, there are other modern wheels that will fit your car. Others within this group can suggest proper alternatives. Be safe; use modern wheels if you want to run radials.
Kindest regards,
Alan Mende Hummelstown, PA