FAA rules generally require the repair to match the new. That is, if the wire was originally soldered, then the repair is soldered. If the wire was crimped from the factory, then a crimp shall repair.
Planes made in the 50’s and early 60’s often used solder cups in their multi pin connectors (aka Cannon Plugs). By the early 70’s, everything was crimped.
Keep in mind that the crimp connectors used in aviation are a far cry from what you can find at Auto Zone. The equipment required for those cost a lot more than a soldering iron from Radio Shack, but then a soldering station used in avionics runs about $12 grand last time I checked, more if it is set up for micro-electronic assembly repair.
Of course now we are way out of the league of repairing the wires on a 4x8 trailer. For this, a crimp tool and some crimp splices from Auto Zone or equivalent will work just fine. Just do not use those EZ (blade) splices where you stick the wires in each end, fold over the cover and pinch with your fingers. No tools required but they just don’t hold up and can lead to other problems, especially if one end of the wire sticks out too far from the connector.