Water of Ayr stones were produced a few miles from where I stay. Quarrying from the river Ayr was halted many years ago, and as far as I know the stocks are all gone. I still see it listed as available in some places, but don't know if that is the real thing. I have a couple of sticks I use from time to time. It is very soft, and I would suggest too soft for everyday use. I only use it for frosting polished brass plates.
For honing, it depends on the fineness of the finish you require.
600 grit diamond stone, followed by 1200 grit, will give a finish good enough for the faces of a graver for turning steel or brass. Those stones/plates are readily available. For finer finish, a 2000 grit diamond stone or a ceramic lapping stone or wheel used with diamond spray (3 micron, down as far as 1/4 micron). If you need a better finish than that, you better order some strong sunglasses…
Hardened work takes a better polish that unhardened material, so, as with grinding, harden the work before polishing. Yes; unhardened work can be lapped more quickly, but it will not take a really good finish or polish.
Other interesting polishing and lapping compounds include traditional powders and polishes used by clock and watchmakers. I'm not convinced they are capable of giving a better polish than diamond spray, though. I have one or two powders, but use them infrequently.
If you have a lot of lapping/polishing to do, you might look at the GRS Power Hone (try H.S. Walsh).
There are also some useful polishing papers, from the finer grades of emery 0, 0/2, 0/4 etc, and crocus paper.
For plastics, there are micro-polishing fluids and pads which give a terrific finish if you have the patience.
Arkansas stone is worth a look too, but is rather expensive, and, in the end, not any better than diamond; and less effective than the finest grades of diamond spray.
The only real problem with all of this is that a really fine finish takes a little time.
Marcus