You need to measure the rims. I have in my garage several sets of 27x1 1/4 wheels that range from 15 mm to 21 mm between the beads. The narrowest are Weinmann concave, and the widest are some that I got from Nashbar. Even the 15mm wide Weinmann has 27x1 1/4 stamped into it. A 1 1/8 tire on the Nashbar rim is barely wider than the rim, but it stays on. If you look at Sheldon's article, you will see that there is a lot of leeway for rim width vs, tire width.