Those should work just fine - have at it
. Refresh the edge on the 1K and refine it on the 4K. Spend enough time on the 1K to get it really sharp. HAP40 is pretty wear resistant, but Shapton GS stones cut even that steel pretty well.
If you're new to sharpening, I'd practice on a few other knives first. For the Kohetsu, paint the entire edge bevel on both sides w/Sharpie, then grind just a little on the 4K first to get a feel for what angle to hold so as to remove the sharpie from the edge bevel, all the way to the edge of the edge. Do this on back 1/3 of the blade, where it's flatter, not the tip area. Do this for both sides, again to get a sense of what angle you need to use to closely match the factory edge bevels. Once you have this feel, then switch to the 1K and follow standard sharpening procedures to sharpen, deburr, and then move to the 4K to refine the edge. Mark has some good videos if you're a newbie to sharpening: knife-sharpening-instructional-videos-for-newbies-t1930.html