As has been said chasing the threads will only work if there is enough material there, but the threads are just messed up.
There is also a little metal piece on the inside of the tube that the end of the screws bears against to protect the tube that fits inside. that will need to come out most likely, especially if you use a regular tap. The homemade chasing tool probably won't require this.
If the threads are too far gone your choices are as have been stated, cutting the next size up thread and using an larger wing nut that will not look original.
A helicoil would be my choice. You can buy kits that come with several inserts, a drill bit and tap and insertion tool. Once you drill and tap the hole you put a little loctite red stud and bearing mount on the insert, thread it in with the insertion tool then let the loctite dry. Then you break off the little tang on the insert that is left behind then you can reinstall the tube protector and you should be good to go for another 50 years.
It sounds harder than it is but the kit will run about $20 to $30 so unless you plan on fixing a lot of these, your best bet is probably to take it to a machine shop with the tube protector removed and with the wing screw and ask then to put in a helicoil and have them do all of the work.
I took a look at a couple of the same types of hi hats and there is plenty of material there for a heilcoil repair.