My suggestion should work fine to repair that. It doesn't look damaged too badly. If you were here I could probably have that fixed for you in a few seconds. Bring it to a place that sells nuts, ask them to size it for you and buy one nut. Wind the nut on slowly by hand, no tools, back it off and on carefully until thread reforms.
Note: The material of the cap is actually brass, still pretty soft though compared to a steel nut.