I'm trying to find out if there is a regulation for the use of USAF/CAP grade abbreviations as opposed to using US Army abbreviations (Capt. John Doe, CAP as opposed to CPT John Doe, CAP).

Air Force Handbook 33-337, The Tongue and Quill, provides an excellent guide to using abbreviations for grade among the services. CAP uses the Air Force style.  This publication can be googled.