Looks to me like Henry is an ordinary vacuum cleaner. The danger with the procedure would be that if the pressure is a bit off, the whole thing might just blow mercury all over the bathroom and its occupants. Or suck everything, water and mercury, right into poor Henry, creating a fire hazard.
My idea would be to try a wide-tipped pipette, if you have one. Drain most of the water first, though. And whatever you do, don't use your mouth to suck.