They'll be fine on your stock rims.

The original wheel size/tires specified in the FSM for 1951 3100 trucks are:

6x16-6 for all four wheels or
6x16x6 front and 6.50x16-6 rear

15" rims were stock on the sedan delivery

You can buy 16" smoothies with new hubcaps from Wheelsmith. If you want to use your original caps with the new Wheelsmith wheels, they sell clips for your caps that will work with their wheels.

1950 Chevrolet 3100 (Ol' Roy)

1939 Packard Standard Eight Coupe (The Phantom) | 1956 Cadillac Coupe de Ville (The Bismarck) | 1964 Ford Galaxie 500 coupe |1966 Ford Mustang (Little Red) | 1969 Pontiac GTO (The Dishpit) I 1979 Ford F-100 | 1976 Ford F-150 (Big Red) | 1995 Ford F-150 (Newt)