This may sound a little odd but I have done it many times.
When you get your new trailer back it up to the old trailer with the boat on it. Front of old trailer is on the ground and new trailer goes over the top of it. Securely chock the old trailer and if necessary put some jack stands under it, leave the new one attached to the tow vehicle. Remove the winch post on the old trailer and attach winch from new trailer to boat .Wet down the rollers and/or skids on both trailers and winch boat from old trailer on to new trailer.
Slow and steady and job is done.