This advice smacks of fraud, and
if it is in fact a CTL, and you repair it and offer it for sale or transfer - you will be in deep doo doo. Subject to prosecution in many states. If you are going to go this route, I suggest strongly that you READ the terms and conditions that you agree to, by taking the check.
For sure you can repair it and use it....but if involved in an accident, that can in any way be attributed to the CTL damages, you can and likely, will be find liable...and without insurance.
The HIN, make, model and ANY information they have on the boat and you will be entered in to the databases available to the insurance companies and made available to other insurance companies.
Whether car/truck/boat/motorcycle.....you WILL have a next to impossible time EVER insuring that boat again. Insurance companies will NOT pay twice. Once totaled, they - collectively are done with that item. To them it no longer exists, and their lawyers are better paid than yours will be.
No need for deception with anyone. Of course the insurance companies share information, and I would expect the loss and related changes of ownership would be reflected in the documentation history.
I did not suggest that the OP try to hide the history of the boat form the second insurance company, just that I believe that the insurance company presented with a good survey of a vessel, is likely to extend insurance for it, even if the insurance company knows it had a bent toe rail in the past, as long as it has been repaired to a surveyor's satisfaction.
The OP has an opportunity to own the same boat with a marred history, plus perhaps $15,000 in the bank. When he goes to the sell the boat, the next buyer will expect and get a substantial haircut on value, due to the history, but he too may end up the smiling owner of a lovely boat for $15000-18,000.
The boat does not have leprosy...