That is done all the time. Many people do not have boat trailers. Their boats are blocked up in marinas or at their homes. Marinas routinely take their trailers(sized for 28 footers) and load different length boats for the purpose of launching and retrieving. They simply pull the boat onto the trailer until the transom is even with the end of the trailer and then tie the bow so she won't shift forward.
If you want to use your trailer to only tow your 12 footer, simply slide the winch stand forward and adjust the winch to make the trailer as short as possible, ideally 12 foot. You may need to adjust the rollers in or out to fit the boat better.
If the bow doesn't quite reach the winch stand, pull it forward until the transom is even with the trailer and tie a safety chain snugly to the bow eye. Now run the winch line around the first roller under the hull and back to the bow eye and tighten the winch. That will usually hold the boat pretty well.
You can also do some sort or rigid winch stand extension to contact the bow. Bolting some 2X4s together around the winch stand with a nose roller, will likely be strong enough
