I have not tried to remove the ice box hose but here are some ideas: It may be possible that the hose is removable from inside the ice box but I doubt it. If not, then you will need to make an access hole for the hose. The best place is probably on the panel inside the swinging cabinet inboard of the nav station. Get one of those 3 or 4 inch inspection ports and cut a hole in the panel. That should give you plenty of access to the hose at the bottom of the ice box. And you can fill the hole with the access port afterward.
One question though. Why are you interested in the ice box hose when you want to pump to the sink on the opposite side of the boat? You should be able to snake a hose up the port side and to the sink.
PS - You should really consider pumping directly overboard rather than into a sink.