Generally you have 30 days to get the tag for a trailer. Many states do not "title" smaller trailers like boat trailers. Generally LEO will accept bills of sale--and you have a certain time to buy the tag--a little different than a car or truck, If--and that is a big IF, you are stopped, the bill of sale is sufficient. In over 60 years of trailering boats, I have never had anyone ask to see trailer registration papers. (I do carry them always. still).
It is extremely important to have insurance on the boat before it is transported. That boat insurance coverage includes the trailer.
I have handled it different ways--one was to have the seller allow the buyer to use his tag. If tags were kept--then it was mailed back to him. I did this when I sold "Thisaway", the last 22. When I picked up my 25, (before I had sold the 22) I used the tag off the 22 trailer--since it was going to be transferred to the 25's trailer.
When I bought the boat in New Mexico, and trailered it to Las Vegas, I used a similar method-the tag which was going to be assigned to that trailer. In Florida you keep the tags, and transfer to another vehicle. Some states the tag remains with the vehicle.
In your case, I would allow the buyer to use your tag to get the boat home--and have him mail back the tag to you--and provide evidence that he had registered the boat in his home or destination state. Provide a written bill of sale, and "permission" for him to use the tag to get the boat home. Also some states separate the sale of the boat, motor, accessories and trailer. Florida is one of those states--if a private sale, you only pay tax on the boat. The trailer tag and tax is separate--nothing paid on motor and accessories.