IS it a float on trailer you want to switch it to or is it a roller trailer.Can the broken trailer be moved at all? This happened to me I used a floor jack 2x6s and cinder blocks {holes face up} I raised the boat off the broken trailer supported by the 2x6s on the blocks then backed new trailer carefully under the boat.The replacement trailer had rollers so it went pretty easy as I backed it up to the first 2x6 the bow was on the rollers a couple of feet I stopped and carefully removed first support then backed up to where the second support was by this time most of the boat except for about 1-2 feet was on the new trailer.I then was able to winch the last couple of feet. This was a roller trailer. When I tried it with a float on it was a little bit of a task as it was very hard to winch it on the bunks. Hope this info helps you.
Without more information, it's hard to make suggestions. Can you move the current trailer? Can you jack up the boat, put supports under the outside edges of the trailer and the keel up forward, and move the current trailer slowly out from under the boat and slip the new trailer under the boat...???
trust me!!!! IF AT ALL possible you want to try to get that old trailer to a ramp and put that boat in the drink...
keep in mind if you are not used to moving around boats in a boat yard this it not as simple as ... " oh yeah... just jack it up".
21 ft could be as much as 4000 lbs. I dunno the boat but still at 21 ft its going to be a "heavy" boat to move. be safe!!