Get some WAGO wire clips (221 series), take a very good look for polarity then proceed on replacing that connector (by exposing new wire, do not reuse last few cm near the burn). You can also buy a fully insulated electric box and wire nuts for it to make it fully waterproof (by putting the wago clips inside the box). If you don't need fully waterproof just take a cable tie and secure the 2 wires together near the wagos so no mechanical force can go to the wago clips. You can then wrap the assembly in electrical tape if it needs to be able to take the ocassional water spray/splash, or if you want to be able to touch it without any worries while powered up.