I am assuming that we are talking of repairing a hole or something of that nature ie not a split or valve problem.
If this is the case I wonder if we could take a lesson from farm tractors and heavy goods vehicle tyre.
Tyre repair people fix these by drilling out the hole with a bit of known size. They carry with them bungs or plugs of that same size and then with a bit of glue added they push the plug into the drilled hole.
Once dry the puncture is repaired as good as welding two pieces of metal.
You can buy cheap lightweight compressors which are enough to fill a car tyre which are about the weight and size of a torch and batteries.
Rubber plugs, a tube of rubber glue and a torch size compressor and perhaps a sharp knife would easily fit into an small aircraft.
Excellent idea gallois, this should be also very easy to accomplish, I found a very good instruction here (for a car):
https://www.instructables.com/How-to-Repair-a-Tubeless-Tyre-Puncture/
And also plenty of repair guides on YouTube.
You can buy cheap lightweight compressors which are enough to fill a car tyre which are about the weight and size of a torch and batteries.
Why not an emergency bicycle pump? They’re cheap, small and lightweight. This can even used to top off the 0.8 bar from the gunk spray. And if you are afraid of eyeballing pressure, there are small pressure gauges available.
https://www.motorradonline.de/test/14-luftdruckpruefer-test/
A bicycle pump would do the job just as well. I just keep getting ads flashing up on my smartphone for mini compressors at around €40.🙂
