Ideally you can go through the grits, start a bit coarse, then go up to finer getting rid of the grooves from the previous step. If you do this be sure to have good ventilation. Preferably a dust extractor. If you don't have that do it outside or in a garage with a mask. Trust me, the fine dust gets everywhere, especially when turning and you get to the finer grits.
It's a real PITA, even with a lathe but it can be done. But you really don't want to be breathing the dust in. If you don't have a dust extractor be prepared for itchy eyes from the fine dust, maybe some swim goggles and a mask at minimum.