This knob in an old trailer of mind broke off. Is it possible to replace it?
I'm curious if the aluminum "thread" that inserts into the knob has a name or standard. You can see what I mean in the first picture.
You can be certain that the thread is a standard size. Take the screw or a similar one to a hardware store and they will help you find a matching one.
As was mentioned in the comments, the attachment looks very much like a standard window crank. I would bet that a search on Google or the like would turn up some sources.
I would try to use Round Valve for plumbing. Something like this and bolt it down really well for a tight fit. To secure the fit, may be even use liquid nails or solder it to the male piece.