Never heard of a cork before except on my dinghy
What's the year, size and make of your boat? My dinghy has a rubber cork on the stern, but that is for another purpose altogether. I have never heard of using a cork on the pipe at the bow. But that could just be me.As for your sink drain hose, the hose should end at a thru-hull seacock. You should be able to just close the seacock, and then disconnect and work on the hose. If there is no seacock, then I would start to worry. I can't imagine a production boat without using a seacock.If the seacock is not easy to turn, or won't turn at all, then be very gentle. It could've rusted or corroded shut, If you force it, you may end up braking parts of it off then you will have real trouble. If this is the case, then you should wait until you haul the boat to fix it.