Raymond, it might work as long as your rims don't bottom out or as long as the tube doesn't squit out from between the tire and the rim and bust a gut.

I tried to put a new "fits all rims" Kenda mountain bike tire on a 26 X 1 3/8" rim. That did not work. the new mountain bike wire bead diameter was too small.

It should be easy enough to try.

One thing I am sure of is that you CAN put a 1.75" tire on an old fat-tire 2.125" rim. I see this all the time on old fat-tired bikes. The narrow tire fits so well on the 2.125" rim that it confuses some collectors who think the old ballooner is a younger middleweight rather than the old ballooner it actually is.

If you really want to go light, keep your eyes open for an old 26 X 1 3/8 roadster-type three-speed. You probably won't find any single speeds because they were mostly three-speeds. Look for one with a coaster-brake style hub. You should be able to find one at a yard sale, flea market, or thrift shop for less than $25.00

Sturmey Archer made this kind of hub for some time. Don't get the more common 3-speed hub without the kick-back coaster brake or you will need to mount hand brakes on your ballooner which is complicated and takes away from the look of the ballooner.