Then you'll have to improvise.
Try holding a ruler against it and counting the threads against a number of mms, or put summat on it, like lead from a pencil and push a piece of paper or card hard onto the side of it so it transfers the marks to the paper, then you can count them at your leisure.
Look really carefully at all the threads to see if, as you say, you damaged any. They should be saveable with a thread file or even a vey small ordinary file, if you don't have a tap and die set.
I can't manage without one of them, I use them all the time to clean threads on both bolts and nuts and threaded holes in stuff.
They all come with a thread gauge. They aren't expensive and you won't regret getting one.
https://www.google.com/search?q=tap...PAAQHaAQYIARABGAnaAQYIAhABGAg&sclient=gws-wiz
To give you some ideas.
A 13 mm nut or bolt head is normally on an M8 thread which is 1.25 pitch.
But as you have a flange nut there, the diameter of what it is going on could be different, so you need to measure across the widest part of the thread on the spigot thing to see what it actually is, as it's been made oval to do the biz in the switch. Next smaller would be M6 x 1
(Next bigger would be M10 x 1.5. but I doubt hugely it'd be the latter. As it's only turning a switch !)
But these are standard sizes, if the size is a weirdo you really do need to borrow a thread gauge.
M8, M6 is niminal by the way, the actual size of the bolt or threaded part will be a bit different, M8 is in fact 7.73mm and M6 is 5.84, as i have just checked from a lot of bolts I have to hand.
Here's how to measure thread pitch if you are having to count them. It's just simple maths really as measuring an individual thread's pitch would be not easy, better to do a lot then divide by the number of threads counted, so if ten threads comes to 15mm then 1 would be 1.5mm etc.
Imperial threads are "tpi" i.e. threads per inch, which is easy to understand.
Best of luck!
