It depends entirely on what other hones you have. You have only mentioned a mystery 1k hone and a Swaty. If that is all you have, then your options are a little more limited. If you did in fact get closer to cutting the bevel with your Swaty than you did with the 1k, then you need to assess whether or not your bevel is fully set. Draw the blade lengthwise along your thumb-nail for the thumb-nail test (TNT) and see if you note any changes in the drag along the length of the blade. Chips/dings in the edge will interrupt the smooth drag. Do the thumb-pad test (TPT) by lightly drawing across and along (remember I just said lightly) the blade. There should be a uniform bite into the pad along the entire length of the blade. Depending on the nature of your arm hair, you might (and might not) be able to shave the hair at this stage with a properly set bevel. If you think you are close, then I would go back to the 1k and spend some more time on that. As you proceed, use less and less pressure. This should help smooth out the rough edge from the Swaty.
Because you said you made progress on the Swaty in a few minutes, I am assuming that you used pressure to accomplish that. Also, did you use it dry, with water, or with lather? Because of the non-porous nature of the hone's surface, water tends to bead and get pushed off quickly. You can overcome this by adding just a little soap, detergent, or lather residue to the water. You don't want shaving lather thickness, just enough of something to break the surface tension of the water so that it forms a uniform layer on the hone.
Anyway, after the no pressure 1k honing, I would go back to the Swaty and do 10-15 no pressure strokes and then stop and strop and shave test. If it doesn't shave, pick up the hone and do another 10-15 and repeat the process as needed. Once you get a decent shave, drop the stroke count down to 4-6 strokes whenever you notice a diminishment in the quality of the shave.
If you do have other hones, then use THEM and leave the Swaty for the touch ups!