re: Removal of abandoned boats from private property......

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Have a piece of property on waterfront that I’m going to start using.

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How long has the piece of property sat "unused"?

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There are 3-4 boats tied up that are half sunk and in bad shape.

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How long have the boats been tied up there?

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It's not a wide or deep bayou.

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Is the bayou on your property or is it simply adjacent to your property?
If these are derelict vessels along a public navigable waterway, you have a couple of options.

You say you're OK with removing them, you just want it done right?
Well, if you do it the "right" (legal) way, it could take you quite a bit of effort and time (spent waiting) that may just leave you in your present situation. The amount of time it takes can vary widely depending on the responsiveness of the agency or agencies that you contact and the amount of time (dictated by law) that any owner or owners are allowed to claim their property. Add any additional time-consuming associated legal formalities and it could easily take well over a year!

If you want it done quickly, then make sure that you leave no evidence after removing and disposing of the vessels. One of the vessel owners may just miraculously appear claiming that you illegally moved and subsequently destroyed their vessel.
If a quick and efficient resolution is what you desire, you could possibly dig a shallow pit, haul the wrecks into it, immediately burn them, and then thoroughly bury whatever remains.

This could be a tough decision and may be one that you have unintentionally already made.
Once you begin doing it the "right" way, it could extremely difficult to change your mind and execute a more expedient course of action!
Good luck to you!