To add my tuppenceworth to the debate, stones - water or oil - are the gold standard and yield the best results on balance. However, if you can find glaziers who replace broken shop (store) windows, they will, in the UK anyway, sell you small pieces of float glass. Spoken to persuasively, they will cut them and fire the edges. Automotive wet-and-dry abrasive sheet in varying grades can then be glued on and used to refine your edges. Easy to replace when worn and you can use them while you save up for the Japanese water stone you really want. BTW, lubricate with 3-in-1 oil, diluted with white spirit.