If the valve stem hole is too small for a standard schraeder valve then a presta valve will probably fit. As for the rims themselves, there were other types of rims/tires available in the U.S. during the ?Single Tube Years? but they were often proprietary and anything but universal. The most popular was the G&J (Rambler) clincher that was developed in the mid-late 1890?s and used a tire that circled around under the inner tube and had a sort of wedge shaped bead that locked it against the rim. If you find a clincher tire that fits your rims the important thing will be the mechanical compatibility of the tire bead with the rim?s bead seat. If the tire fits but doesn?t lock in place it may be best not to ride the bike with that combination.
Typically U.S. single tube and period clincher rims while called out as 28? equate most closely to a modern 700c rim diameter which is smaller than the American 27 inch size and the English and most European 28 inch tires sizes. Interestingly I have found that Canadian 28? clincher tires and rims come the closest to matching the American single tube tire and rim diameters.
I hope this overview is useful, but in the real world if often comes down to the trial and error method when trying to find tires to mate to old rims.