E-bikes are motor vehicles and can't be used on bike paths in NY state though they are street legal if registered. NYC park police actively ticket E-bikes on the west side.
Do you know if the restrictions apply to the electronically assisted "e-bikes". They pretty much operate like a normal bike, but require minimal effort to go up hills.
I do know about this restriction. You can get your physician to write you a note stating that you need an assisting device for locomotion purpose and show this to the officer trying to site you.