You want singletube tires. Are those rims about 25" on the outside? those fit a 28" (outside diameter) singletube tire. Coker has them, so does Memory Lane. There's a little machine shop that makes them too, I'll look up the name when I have a minute. They're kind of expensive, like $300 a pair. Memory lane has some tubular singletrack tires that fit for less but they don't look exactly right. Sheldon brown has a bit about how to make your own out of canvas and latex. If they're 24" tires (with about a 21" rim) first flight has a used pair for $100. They glue on with regular tubular glue. The guys at www.thecabe.com talk about using some sort of 3M adhesive. I think they used some sort shellac back in the day.
The rims might be steel sheathed wood. That was popular back then. Folks just didn't trust that skinny steel shell.
Compressed air should be ok but don't blow the wooden parts clean off the bike. The rims look to be in great shape if they are all wood. Those usually warp and split.