Approach Controller described a conflict when a Lifeguard aircraft was approved for other than the primary runway resulting in a circling maneuver to lose altitude and leading to the event.

Narrative

Arrival called and requested approval for a Lifeguard [aircraft] to land on Runway XX; we were landing and departing Runway YY. The aircraft was very high [and] called me over ZZZ airport at 6;000 FT. At this time; Satellite called and requested 'block ZZZ.' I figured they knew about the Lifeguard from the Arrival Controller who was required to point out the aircraft since he would be descending into that airspace. I acknowledged the ZZZ block. The Lifeguard said he was too high and needed to circle; I asked which way he would like to circle. He said through the final or he could take Runway YYR; I said Runway YYR was closed but he could have YYL. He wanted to stay with Runway XX. I issued the Lifeguard a right 270 turn after flying through the [Runway] XX final and cleared him to land. At this point I called East Departure and advised of what the Lifeguard was doing and said; 'Do you want to tell Satellite also or should I?' They asked to block ZZZ. East Departure said; 'I have nothing out there; point out approved; I will tell Satellite.' The Lifeguard was in a northeast turn; when Satellite called and said they could not get contact the ZZZ departure. My Supervisor said [to] ask if the Lifeguard could cancel. I asked the Lifeguard [if] he could cancel IFR [and] he responded that he could. I canceled the IFR services and re-cleared him VFR to Runway XX and cleared him to land. Shortly after; I saw the transponder of the departing ZZZ departure and had to give a traffic [point out] to the Lifeguard. He did not see the aircraft and I ended up giving the Lifeguard a 'traffic alert' and an evasive turn until he saw the departing aircraft. I estimate 100 FT and 1/4 mile as their closest proximity. I believe that all 'off runway' arrivals and departures should not be allowed. This runway is a hazard and should never be used unless we are using it as the primary runway due to wind.