The simple answer is that your dentist would not visit the yard.
Strangles spreads very quickly and an individual moving from one horse to another can pass blood or saliva which will exacerbate this process. Also, some horses that have recovered from strangles can still harbour the Strep. equi with no outward clinical signs.
Your dentist will take great care to clean and disinfect their tools after each horse, but, even with these precautions the risk of spreading strangles would be too high to take the risk.