Replacement nut for output jack?

The nut for the mono output jack on my JP15 has worn out to the point where I can barely keep it on the thread. I’d like to replace it before I lose it and the jack goes all loose or whatever.

I imagine these are pretty standard for all guitars, but just wanted to check before buying online (since I can’t seem to find such a small nut for sale at my local Home Depot).

Stewart-MacDonals seems to offer them in 3 different sizes;

#1231 For SAE pots/jacks such as CTS and Switchcraft with 3/8″ x 32 thread.

#1229 For metric pots such as Alpha with M8 x 0.75 thread.

#1239 For metric jacks with M9 x 0.75 thread.

Can someone confirm which one would fit a Music Man? Alternatively I’d be more than happy to buy direct from EBMM, if they sell these.

Thanks!