Not that it answers this question, but just for interest's sake, in the Royal Navy dental officers wore orange distinction cloth. The RN dropped distinction cloth around 1959/60 (about the same time the RCN did) for everyone except the medical branches. I'm not sure if the RCN ever even had dentists as the responsibility of naval dental care in Canada was assigned to the Royal Canadian Army Dental Corps a very long time ago (hence the reason all dental personnel today wear Army DEU).
The Canadian Coast Guard still uses distinction cloth and for the most part uses the same colours the RCN used to (i.e. pruple for engineering, white for supply, etc). Of interest is that orange is now used for pollution control officers.