If you already have the seahare I'd just transfer him over until the tank is clean.
Sort of a catch-22 though, the one good thing hair algae is good at is giving a home for 'pods to replicate en masse, I bet your seahorses are eating like kings at the moment.
Thing about seahares, unless you get one that learns that nori is good for them (not all do, I've only ever kept one or two that figured it out), they'll starve when the hair algae is gone. So it's better for them if you can transfer them into a hairy tank once their current abode is clean.