Tower Controller described an event when an emergency light twin was cleared to land on an intersecting runway with Air Carrier traffic landing on another with no assurance of required runway intersecting clearances.

Narrative

Runway XX was the active runway. Aircraft Y; BE76; advised approach he had a rough running engine but was not declaring an emergency. Aircraft X was on a 4 mile final to Runway XX. Aircraft Y checked in with the tower 6 miles Northwest of the airport advising he shut down 1 engine. I advised CIC to activate the ARFF equipment and declare an emergency. I issued a wind check to Aircraft Y and asked if he could accept Runway YY to get him on the ground ASAP. Pilot advised he was able to land Runway YY. Aircraft X landed Runway XX and appeared to be under control taxing. I asked pilot of Aircraft X if he was able to hold short of Runway YY; intersecting runway; to ensure separation with the intersecting arrival of Aircraft Y on Runway YY. Pilot of Aircraft X advised he was unable to accept that instruction. I observed the Aircraft X turning Bravo Taxiway short of Runway YY when Aircraft Y was over the landing threshold of Runway YY. There was no loss of separation. Recommendation; issue a go around to the aircraft landing Runway XX; not declaring an emergency (Aircraft X); to ensure separation.