think about it for a moment....

Without hesitation, I'd stand on the board.

Consider the forces that normal sailing puts on the boards, LATERALLY for the most part, what, thousands of pounds? And you're worried about YOUR weight? I wouldn't use 'em for a springboard, but yeah, I'd stand on the board to right the boat...

Better to stand on the board which is reinforced for big loads than the hull which is only reinforced to resist being pushed thru the water.