I doubt if my dealers would mount on a 4" rim.
However, both of the local dealers have mounted new radial tires on 4.5" rims, and both have been willing to use tubes.
One set of wheels needed tubes, and the other set did not need tubes.
The set with tubes is now about 12 years old.
If you are going to do normal speed, normal road driving, you might be OK with 4.0" rims.
However, it would be nice/safer to hear from people who have mounted this size radial on a 4" rim.