No.  Dentistry falls within New York's definition of veterinary medicine (see, Section 6701), so you must be a licensed veterinary professional to perform it.  It is not legal for an unlicensed vet assistant to do so.

Section 6713 of the Education Law addresses the types of duties that may be performed by unlicensed staff:   An unlicensed person may provide supportive services to a veterinarian, including but not limited to administering oral or topical medications, incidental to and/or concurrent with such veterinarian personally performing a service or procedure, provided such supportive services do not require the knowledge of veterinary science.  

The supervising veterinarian is responsible for the proper delegation of duties to unlicensed staff.  If a veterinarian has staff performing duties that are not permitted by the provisions of the laws and regulations cited above, the veterinarian may be charged with professional misconduct based on a charge of “delegating professional responsibilities to a person when the licensee delegating such responsibilities knows or has reason to know that such person is not qualified, by training, by experience or by licensure, to perform them.” [8 NYCRR Part 29.1(b)(10)]

More information on the duties of LVTs and unlicensed staff is available in our summary of the duties of LVTs and unlicensed persons