cold temperature can't "flow" into a warmer object, in this case, the person's hand. the heat energy of the hand gets transferred to the colder object, the ice.
push the cork underneath using something that's thin and then it won't take as much space and it'll measure a new volume of the cork reads. then you subtract to get to the cork and volume and then divide the mass by the cork and volume and then you have the density of a cork.
i hope this ! have a nice evening.