You can get them on eBay or amazon, even local car parts shops should stock them. They are called super seal connectors.
Here is a link showing how they work.
Do you have a soldering iron or can borrow one from a friend, neighbour?...
Cut both cables, strip the wires, twist together, solder, insulate with
heat shrink sleeving or Sugru or Araldite or insulating tape.
If you are in a real hurry...
Cut both cables, strip the wires, twist together, insulate with some form of tape.
Re-do later with something more permanent when you have the time.