I don't know what you mean by "convex sharpeners" but I think you have everything you need. Doing it by hand is just a matter of spending more time.
I use a 1x42" belt sander on mine, and unless I do something stupid (which I have done plenty of times) leather belts and compound are all I need. Unfortunately, I have had to bring out the gritted belts on mine more than once....but I don't want to get into that
I don't have one of those gransfors stones, so I don't know how coarse it is. But, I am guess that you probably only need the finest side of it. Sharpen in circular motions. Depending on how smooth it is, I would move to finer grits of sandpaper, and end up on a leather strop.
Depending on what the edge is like, you could possibly get away with just the strop, or just high grit sand paper and then strop, etc. Only the person with the axe in hand can tell.
Of course, you are always welcome to ship it to me and I can ship it back out the next day.
For what it is worth, my "Field Kit" is two waterstones 1000 grit and 4000 grit, and a leather strop loaded with compound. It works great. However, if I can keep for sharpening in the field I will because I know it will only take me 30 seconds when I get back home, and I would rather enjoy the woods doing other stuff.