I wish to know if we have the ability to hide certain subclaims from the map - completely, or until the player loads the map.

I wanted to sell scrolls of teleportation that lead to certain waystones in the dimension (mainly near dungeons, which would help new players to quickly speed-run through them, without spending time finding them). They're meant to be one-time use for those who aren't in my party, and in order to do that, I claimed the chunk where the waystones are (as well as protecting them from griefers)

However, the claim is visible on the map, meaning that all players will know where the waystones are located, meaning that the position of the waystone is revealed, and it's useless to sell scrolls of teleportation.

You can limit claim server-client synchronization to "OWNED-ONLY" which makes OPAC only sync your own claims and server claims.
Otherwise, no, you can't hide claims because doing it properly, not just visually, would affect performance too much.