IANAL, but I think recording the conversation surreptitiously is legal in NY, as long as one party knows they’re being recorded.

At the US Federal level the law is "one party consent", meaning that someone who is a party to a private conversation can record it without requiring the approval of the other part(y/ies). You can't record someone else's private conversation without approval, but you can record those you are a party to.

Some states have stricter "two party consent" laws which require both/all parties to approve, which is why most national companies put automated warnings in their phone systems if they're recording any calls.