Broken tenon

[Emperor Zurg]

I have delrin rod here all the time. I could send you a couple inches for the postage if you have a way to machine it.

[Nature]

I have delrin rod here all the time. I could send you a couple inches for the postage if you have a way to machine it.

I do not have use of a drill press or lathe to turn it. I could chuck it in a drill clamped in a vise and use a sharp chisel or file / sandpaper to get it to proper diameter.
Or, if the rod is only slightly larger diameter than the existing tenon, I could bore out the shank mortise and the current bit to fit. Then after cutting to length, glue the bored insert bridge into the stem?