I say, spray paint the seacock to match the interior hull color, then repress all memory of it.
You could ask the local boat yard if they would be willing to lift the boat up just past the thru-hull and let you work on it while suspended just above the water. A partial lift may be much less expensive than a full haul depending on the yard and whether they have their equipment readily in place.
Or . . . go to shallow water at high tide, wait for low tide so you're high and dry, work fast? Some people bottom paint their boats this way, right?