I’d keep it as the Saracen UU (or Arab/Bedouin if they are split), just rename it “Bedouin Raider”. I described my idea for a more historically accurate unit called Mamluk (to avoid confusion with the unit formerly called Mameluke) a couple times:
There weren’t any Woad Riders in AoE2 time period. It doesn’t make much sense to give them to other civs.
There’s an idea to make the longship a regional Galley line upgrade:
I’d say it’s more of a Western thing, Central Euro civs like Poles and Magyars are fine with Cav Archers flavour-wise.
(Curiously enough, they could also be included in a hypothetical Syrian civ – the video discussing warfare in the Fertile Crescent that I watched recently mentioned that Syrian ghulam riders switched from bows to crossbows for some reason, I don’t remember why exactly)
If it isn’t just a Cav Archer reskin, perhaps something like a weaker Conquistador?
While not Japanese per se, I’d be open to see Emishi and Ryukyuans at one point (I do remember you dislike the second idea). Emishi especially could cover stuff like mounted samurai who don’t fit the current Japanese civ gameplay.