When I bought my sigma, one of the joysticks was broken and I put a top from a children's felt pen on what was left. This works fine for mine, but it depends how much of a stump is left. As its a purely physical problem you should be able to come up with some creative solution. Maybe using a substance that will mould to the shape of the stump and then harden and be glued on - at least enough for a pen top to be fitted. Think dentistry and tooth crowns!!! And don't miss the ring mod knob - its the same size as all the other small ones. Only the sound is far bigger!
Best of luck.
(two joysticks is double happiness)
"On the following day , the sorcery undespairingly continued: I changed my series, chose other sequences, cut other lengths, spliced different progressions, and hoped afresh for a miracle in sound." (Stockhausen)