If your MD22 setup is the same as mine, the heat exchanger is a long assembly runninh the length of the starboard side of the motor.  
Most of the heat exchanger is for cooling water, but the aft-most 6 inches is an oil cooler.  
While I'm not totally positive, I do believe a good amount of oil will stay residual in that oil cooler.  It would require disconnecting and bleeding a hose (or both hoses) circulating the oil through that cooler to get everything out.

Of course, your mileage may vary and I just know about my particular setup :)

Gary W.
SM #209, Adagio
Tortola, BVI