I have seen decanters where a broken, or misfitting peg has been replaced and have misgivings about the process, but pragmatically it would 'improve' the stability of this particular piece and avoid further damage.
I have asked restorers about the process myself and always fought shy, but effectively the old peg has to be ground back to get a flat surface; a new piece of glass having a corresponding flattened area added by glueing, and then the new peg ground to fit.
Provided that the repair is obvious, then nobody is going to be fooled into thinking it original and therefore perfect. When that is the raison d'etre (I'm thinking of others here) then the problems begin.
If you go along the route of repair and use in this case, say a piece of clear glass, then that corresponds with, amongst others, the English Heritage idea of making repairs obvious - no attempt to deceive (if an item is going to be sold) and the possibility of re-doing it in the future should ideas change.
I have discussed this in the context of the general as well as trying answer the question in order to explore the rammifications of re-pegging.
I hope my comments help, Nigel