Hi Dan,
I have done this on more than one occasion. It's kind of fun.
A tube is a tube - kind of. just decide if you want to use latex or butyl, and what size you need, and buy one at your LBS, a standard clincher style tube.
Tubies do vary quite a bit in tube size, so just taking a tube out of another tubie, different brand, different size, is less likely to get you the right size tube than matching the one you have with a new one at the shop. Size is the only thing that matters, and really, it doesn't matter much.
Use a strip of cotton seam tape to cover the sewn casing. Go to a sewing supply shop or a tailor, tell tham what you are trying to do, and they can hook you up. Glue the tape on with tire life or liquid latex.
Dental floss will work fine to re-sew, or take a sample thread from your tire remnants to that same sewing supply house. Make sure to glue down the bitter end of the thread with the tire life/L latex.
Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
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