TRACON Controller described emergency event when helicopter required an immediate return to home base and conflicted with a small transport in another sector.

Narrative

Aircraft X [helicopter] on an IFR flight plan at 4000; northbound over ABC VFR Checkpoint; declared an emergency due to a transmission failure. He requested vectors to ZZZ for a landing. I assigned him a 090 heading to maintain 4000. I quickly advised the two adjacent sectors and the Tower at ZZZ of the situation and observed Aircraft X turning toward ZZZ and descending. At nearly the same time I observed the limited data block on Aircraft Y and issued the traffic. I believed that the pilot said 'contact' with the traffic and I told him to maintain visual separation. At the same time the adjacent sector Controller; who was working Aircraft Y; issued a turn away from the traffic. The helicopter continued in to land safely at ZZZ. Upon further review of the tapes; the pilot actually said 'no contact' with the traffic. Recommendation; the situation was one in which there was little or nothing that I as the Controller could have done to change the outcome. The Pilot was unable to comply with my control instructions due to his emergency and needed to get to the airport as soon as possible. Aircraft Y was already airborne when the situation developed and was vectored away as soon as possible. My incorrect hearing of the Pilot was almost irrelevant due to the fact that separation had been lost by the time I tried to issue visual separation anyway. Emergency situations can only be seen as a time in which to do your best to keep aircraft apart and get the emergency aircraft to the ground as soon as possible.