For anyone else reading this thread the wires can be terminated by using a plastic card something like a credit card when there's nothing else available.

Cut a small slot about the thickness of a hacksaw blade and about 10 to 15 mm long into the plastic card. The length and width of the slot may vary slightly, but keep the slot as narrow as possible. To ensure the correct slot size check that the slot will fit past the plastic up stand on the terminal and down over the metal contact that pinches the wire. Check this before you attempt to terminate the wire.

Cut the wires to be terminated to length leaving enough length for the wire to overhang the terminal by about 5 mm. Don't be too stingy and cut the wires nice and neat and short. There will be another time when you need to re-terminate the pair so leave as much cable as you can as a loose tail prior to the terminal.  A longer tail makes it easier to work anyway.

Place the wire across the mouth of the terminal and press down with the card as you would for any other termination tool making sure the edges of slot you cut in the card pass down either side if the metal contact. Take it carefully being careful the card doesn't twist and slip past the wire without pressing it into the V slot in the metal terminal that pinches the wire.

This part should be obvious but when the wire is pushed into the V slot on the terminal the metal terminal cuts through the plastic insulation to make contact with the wire. There is no need to strip the wire first, though if you did it shouldn't matter. Also pushing the wire down with a screwdriver can result in the screwdriver blade getting jammed in the V slot and opening that slot up this making it difficult to get a successful termination and you may need to replace the jack.