That occurred to me as well.
It would be hard to exaggerate how limited I am on space. A really small benchtop lathe might do the trick. I'm not quite sure about sticking my toe in that pool just yet!
If I want to make chisel handles I'm probably best off making them using the Smalser method. I believe Aldren Watson also describes this, using a jig called a "turning box" or something like that.