With the tire mounted on the rim and properly inflated, I measured the outer rim width in several places using a dial caliper and the average value was 25.9mm outer rim width. Using 26mm as the value and subtracting 5mm as you suggested, we get 21mm as the anticipated inner rim width. Using these factors given at the Sheldon Brown website: "...A general guideline is that the tire width should be between 1.45/2.0 x the inner rim width...", the range of recommended tire widths would span:

21 X 1.45 = 30.4mm or 1.2 inches

21 X 2.0 = 42mm or 1.6 inches

Someone here stated that Sheldon's upper limit tends to be "conservative", a bit low perhaps. Alright I definitely wouldn't want to use a 26 X 1.125 tire and a 26 X 1.6 would work just fine as far as fit goes and I probably wouldn't want to go any narrower on the width.