Well since the .22 Jet was mentioned, the idea of swaging down jacketed bullets has occurred to me as well. The cartridge requires .222" diameter bullets. Hornady was the only maker and the haven't made then in several years. Too busy making bullets for AR's I assume.
Sierra makes a .223" 40 grain Hornet bullet, SKU# 1100 but they are difficult to find and possibly out of production as well. Some people report that as long as you are not loading the .22 Jet to the max, there is no problem shooting .223" bullets in it.
I would guess that swaging a lightly constructed bullet that is designed for varminting down by .001" or .002" would not require a lot of pressure with a decent press. If the supply of Sierra .223" bullets also goes the way of the dodo and we want to keep our .22 Jets shooting, swaging may be the only option. Hopefully accuracy wouldn't go out the window from jacket/core separation in the swaging process. Experiments will be in order.