Yes. New Hampshire has a unique statute that actually provides some protection to property owners who do in fact post their property. That is why if you hike or drive around the state you see the no trespassing signs. Yes, by all means post the property. AND also make sure you are insured against the risk, just in case.
The actual language you want to use is "Do Not Trespass". They sell these signs in most hardware and home repair stores in NH. If you want to also post a "Swim at your own risk" sign that's fine.
I do not see how a warning sign is going to encourage anyone.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.