While short notice appointments are harder to get, they are by no means not possible.
Contact a few women in NYC that you would be interested, explain that you travel to NYC, but your schedule is unpredictable. Ask if they might be ok with you trying to book last minute, as long as you get pre-verified.
Some will tell you they never take appointments with short notice, or they always book up early. However, many will tell you not to expect them to be available, but it doesn't hurt to ask.
Then, when you want to schedule, since you already introduced yourself and got pre-verified, there is no waiting for verification. It removes an obstacle and comes down to her availability.
You still might not get anyone, but you have a better chance.
Also, check the sires that offer "available now" sections.
You will have better luck with agencies than with indies, I think