I have always boiled out the system with a bilge pump, a bucket, some hoses etc.. I pulled the impeller, covered it up, plugged into the raw water inlet and picked up the return to the bucket before the turbos. Circulate until it stops foaming and then neutralize it. Make sure you pull all of the zincs and replace them with brass plugs or zinc ends. I used a phosphoric acid product from Home Cheepo with some water.
None of our exchangers were removeable. That sounds like a bigger pain than boiling out the whole system (hits all exchangers by the way).