You can pay for the cremation as originally intended and authorized (assuming you weren't charged for cremation services when the vet originally took your credit card information), or you can withhold payment and force the veterinarian to have the remains declared abandoned. This is an official procedure in which you are notified by mail that the "abandoned" remains will be handled in whatever manner the hospital or clinic normally uses if you do not claim them within a certain amount of time. The vet will still be entitled to payment for services rendered, and s/he may or may not try to collect any payment due through an agency or legal avenue. See NY Agriculture and Markets Law, Sections 331 and 332 at
https://www.agriculture.ny.gov/AI/AILaws/Article_26_Circ_916_Cruelty_to_Animals.pdf.
In either case, you can register a complaint about a veterinarian or practice with the NY State Education Department, which can investigate and impose penalties since it's the licensing body for professionals in New York. Their investigations can take some time, but they do get done. See
http://www.op.nysed.gov/opd/rasearch.htm for a list of previous enforcement actions, searchable by the veterinarians' last name.
This page has basic information about investigation and prosecution of professional misconduct in NY State:
http://www.op.nysed.gov/opd/. You can get phone and email contact information there.
This is a link to the complaint form instructions:
http://www.op.nysed.gov/opd/complain.htmAnd this is a link to the complaint form itself:
http://www.op.nysed.gov/documents/opd-complaint.pdf