Inner Tube Replacement
650c x 25 or so should work fine as a replacement for that if all else fails...  This is because they are the same ISO Diameter.  That's an International Standard for measuring tires that takes the diameter of the bead as the measurement, since that's the primary interface from wheel to tire.  Most tires are labeled by their inflated diameter, + or - some cheating on sizes, deep tread patterns and just generally not having good standards in the industry among different countries making them.  ISO takes none of that into account and simply measures where the tire meets the rim.

Both 26x1 and 650c are 571mm ISO.  The second number in any of the Metric tires is simply the width.  Your 26x1 is about 25mm wide, so you should look for a 650cx25 tube, or thereabouts.

One more thing, I say that size or thereabouts because tubes are rubber.  They stretch.  It usually isn't a problem if they are just a little big or a little small.  Given the choice, err on the side of them being a little big.  So even if the closest you can find is 26x1.25 or 650cX28, that should work fine too.