David,
The 4" rim (4" "section width") is for a 6.00x16" tire (standard on 1/2 tons, front and back, through 1953); the 4.5" rim is for a 6.50x16"; and, the 5" that you describe is for a later/newer wheel/truck (no hub cap clips).
In 1954, the section width of standard wheels was 4.5" and was most commonly used with 6.50x16" tires (even though 6.0x16" was standard).
You are correct: get matching 4.5" section-width wheels for the clips and you will have the ability to use the same-sized bias-ply or radial-ply tires. If you will be buying used wheels, make sure the seller measures the inside section-width at the same place that you are measuring.
Tim