@Danlebarbare,
Well Dan, first find a multimeter somewhere and confirm that the potential between the two 115-v "hot" wires is indeed 220 v. Then to be absolutely sure not to kill yourself, confirm that the "cold" wire goes to cabinet frame, to the mid or "ground" connection of your 110-v outlets
Note: When a load is applied you might detect a small voltage between the two "grounds"
Depending on the load presented by your compressor etc and whether you have other protection upstream, your safest bet is to connect the new outlet at the output side of your two breakers