You obviously must be aware of the difference between WAC and ANC, so I can already confirm you that each organization had its own uniform and its own insignia ! WAC personnel did not use Medical Department insignia, for sure ! I have never seen WAC medically-related insignia, and I'm pretty sure there were none .
WACs served in a large number of various jobs, and were employed by the Army, the Army Air Forces, and by the ASF . Apart from a great number of different jobs available to them, WACs active in 'medical-related' jobs mainly served as enlisted personnel, i.e. Technicians for laboratory, surgical, medical, x-ray, dental work, and sometimes as ward clerks, and only occasionally as assistant Nurses . The only exception I know of is that some WACs were recruited and commissioned for work in the Sanitary Corps and the Medical Administrative Corps, and for teaching . As a matter of fact, the AAF were the first to use WACs on a large scale, even providing them with better conditions than the Army (this was later solved by the Army) . Nevertheless, it should be underlined that only a small percentage of WACs were medical specialists (less qualified and less trained as opposed to ANC and MD) . Another reason was that it was often difficult to meet the Medical Department's personnel requirements . WACs were however never part of the Medical Department .
ANC personnel mainly served in the Medical Department (of course they did fill in administrative jobs as well, but within the Department) . Nurses served as Medical and Surgical Assistants and Technicians, filling in a large number of important jobs, moreover they were usually better trained, and large numbers came from the Red Cross or the private sector with a good working experience (which WACs lacked).
I will not go into the political aspects of the time, the 'technical' requirements of the MD, the competition between Army and AAF, and the conflict between WAC and ANC, with changing views from The Surgeon General on general policy toward employment of female personnel in the US Armed Forces .
I hope the above answers your query . If you need more, let's hear it .
Kind regards , Alain