I'm going to answer the question the best I can, but to honest, I haven't used 16" '40 rims. I've only used 15" because the 16" are only 4 1/2" (/) wide.
Also, I don't know what the recent outbreak of original steel wheel and radial tire paranoia on this and the streetrod web site is all about!!!!!!
I'm a past and present oval track racer and recently retired from working 27 years at one of the worlds largest tire companies research and development centers. I spent ten years as a subjective evaluation performance tire test driver and the last eight in the racing division. I don't just putt-putt around in my stuff, I drive the hell oughta' it!
Five of my eight old Fords run stock old 5" or 5 1/2" wide x 15" diameter, 5 on 5 1/2" bolt circle rims with riveted centers that take the '48 and earlier hubcaps. Radials on all of them with no tubes, no welded/brazed rivets and no silicone gasket maker anyplace.
I've experienced no loss of air (tire pressure), no wheel center failure and no rim shell cracks or bead leaks. Maybe I'm just lucky? I don't think so!!! I do my homework!
Don't expect Bubba, at Joe's Tire & Rim, is going to look out for your best interest and welfare. He's paid $8-$10 an hour and isn't the sharpest knife in the drawer.
So with that said, here's the process I go through for rim selection, preparation and tire mounting:
1) Be selective in picking your rims. Check for rust around the valve stem hole and bead area. Pass on those that are thin or have excessive rust pitting in these areas. These are the rim parts that keep the air in the tire!!!
2) Look for lug nut holes that are worn oversize. Nuts might pull through the oversize holes when cornering and won't draw up on the hub evenly.
3) Bolt them on the front hub of a vehicle, spin and check
for lateral and radial runout.
Use the worst one for the spare in the trunk.
4) Sand blast the rims that make the first cut. Reinspect for any possible defects that were masked by old paint or dirt. Straighten rim mounting flanges and de-bur any sharp edges with a file. This will eliminate bead cutting when mounting tires.
5) Prime, paint and you're almost ready to mount tires.
6) I prefer using fresh short rubber valve stems. They are more compliant and will fit the rim contour better than metal ones with rubber gaskets. This helps to prevent slow leaks.
7) Now we're ready to mount tires. I mount all my tires in my shop on a carpet. I lube the bead seat area of the tire with waterless cream hand cleaner. I use two tire irons, one spoon straight and one spoon curved. I wrap'm with duct tape to prevent breaking the paint.
8) Without the valve core installed, inflate 'till the bead pops and let tire deflate.
9) Install the valve core and reinflate to desired pressure (NOT THE MAX PRESSURE LABELING ON THE TIRE SIDEWALL!!!!!). Check the sealing of the core and stem for leaks. I use dish washing liquid and H2O in a spray bottle. Do the same in the bead seat areas.
10) ALWAYS use a valve cap with a sealing gasket. This is your secondary sealing system in case the valve core leaks!!!!(and you will find brand new leakers!). Also, heavy weight valve caps (dice, 8-ball, piston, etc.) will effect the assembly balance, so put'm on now!
11) Take the mounted assembly to a tire shop that has a CALIBRATED tire balancer and correct cones to center the assembly on the machine arbor. Dynamic balance will usually require weight inside and outside. Static balance can be done for those that want weight on the inside only.
12) Mount the assembly on the car using lug nuts with the correct chamfer angle!!!!! Lug nuts are made with different angles and after 50 years the ones you have might be wrong or a mixture of correct and wrong!!!! I WD-40 the studs and nuts to obtain a more consistent tightening torque. Use cross pattern for nut tightening.
13) After you drop the car off the jack, recheck (because it will change) the tire pressure with an accurate tire gauge and you're off to the races!!!!!
14) Recheck tire pressure frequently. Significant outside temperature changes will cause tire pressure to change by many PSI's.
Hope this helps!