Switch in unit doesn't involve a change in awarded AFSC. The gaining unit will be putting you on its rosters in your current AFSC if such AFSC appears on its unit manning documents and it is vacant in need of a person to place in it.
Based on previous thread you are attempting to retrain (cross train) out of your current AFSC (loosing) into a new AFSC (gaining). AFI 36-2626, Chapter 6 addresses the AF Reserve Retraining Program. I suggest you read Chapter 6 prior to contacting the 304th.
FYI: Chapter 7- Air National Guard Retraining Program.