Have you checked the FMDAC's state-by-state listing for NY ?
It says beaches only. But strangely, when you click on the state's name, to read the expanded version, it doesn't say that. It says some parks ok, some need permits, etc... Utterly vague, eh ? So if you go to click on the EVEN MORE expanded version: the link that would supposedly lead you to chapter and verse of where it talked about any supposed permits. Or any supposed fees for said-permits. Or anything that said beach only. Or listed parks, etc... ANYTHING that says what the FMDAC single-sentences answer just said. But alas, it's a dead-link.
I suppose you could go to NY state's park's dept. website, and do a key-word search on "metal" or "detecting" or "detectors", and see if anything actually exists (versus silent on the subject).
Unfortunately, a lot of the FMDAC's well-intentioned list, got it's "yes" or a "no" and the single type of "check at each kiosk" answer by ...... you guessed it: Asking. And some pencil pusher, perhaps envisioning geeks with shovels raiding priceless historic sites, gives an easy answer. Yet if you go to sleuth further, you see no actual "no md'ing" rule exists. Barring something ancillary that a bored pencil pusher applies to your "pressing question".
If you find that the NY park's state parks do NOT contain any real true "no md'ing" rule (ie.: silent on the issue), then presto: It's not prohibited.