-
I rather like 26x 1.25", at least I would if I could get decent tyres in this size.
It has never occurred to me that they are too narrow, but I realise that's just my viewpoint - possibly dating from a time in the past when our roads weren't quite so badly broken up.
So I suggest you try those wheels - anyway, that would tell you whether you like the bike in practice before you go to a lot of trouble over it.
I suspect that back wheel is dished and spaced for a five block - your derailleur is probably a 3 speed for a 1/8" chain. This may well involve some modification, but I'm sure you will want to keep that antique rear mech.
A small point - be careful to preserve that gear control cable. They can fail and it will be difficult to replace since the positions of the 'nipples' which fit into the pullies are critical. Make sure the derailleur end on the cable is well lubricated and not chafing.
These are 26x1-1/4
They kind of fit but they deserve the real deal! I think the current ones are a bit narrow