Wish you had asked 3-4 days ago. I just used loc-tite on the bolt handle for my Benjamin Discovery air rifle and I think it might have been a 10-32 thread.
It's chrome, but it's shaped something like the picture you posted except the knob on the end is a hex shape.
You could call Crossman and ask what the thread size is. (part #
392LE-009).
Would a cleaning jag work?