It depends on how frequently you need to desolder SOT-23-3. For occasional repair work, simply lift the single pin with a bent mounted needle or fine tipped dental pick while heating it with an ordinary chisel tip bit (wide enough to bridge the other two pins when you do the other side), and wick off the solder from the lifted pin, possibly sliding a kapton shim under it, or prod it and check it flexes once its cooled, to guarantee its free, then heat up the other side and slide the SOT-23 off its pads.
However if you've got thousands of them to do, e.g. a production run of hundreds of boards each with tens of the wrong part fitted due to an assembly or specification FUBAR and you've been left holding the baby, a dedicated desoldering bit would be a worthwhile investment.
Ygi's suggestion of machining the tip of a bit to suit could work, but if you don't send it out to get the cut surfaces heavily nickel plated as a barrier layer, then hard chromed where you don't want it to wet, it will have a short life due to the exposed copper core eroding.