You will get some opinionated answers here for sure, but I'll throw in my 2 cents to help a bit.
We talked about doubling the grit between stones in a progression? My personal rule is to stay around a 4x jump, but a 1k to 5k jump should be fine as well. It's just not as nice as a smaller jump, and takes little bit longer. The main thing about taking big jumps is that it takes longer to polish the whole bevel and if you are not experienced you may very well mess up the edge. Too big of a jump and you will never get out the previous scratches, and when it comes to razor honing, scratches are bad. For a kitchen knife making big jumps isn't as bad because a toothy edge is often desirable.
The Shapton 15k pro is great for finishing razors before going to the strops, and I prefer the 16k Glass for finishing kitchen knives. (some people find the 16k glass to be a bit finicky for razors, I included, but the 15Pro is a dream). You may very well finish your razor on the 8k ss if you want as long as you are following up with a good stropping progression, starting with no finer than half micron. Please remember though, razor honing is much different than kitchen knife honing, although much of everything carries over. Hope this helps!