Hi,
I got my first puncture on my first tour (dark forest in the rain, end of a long day...) and had exactly the same experience as you. Fortunately I managed to use a notch on my metal tyre lever to drag the bayonets together (after also first injuring my thumb). I connected one side then wound the shifter round to get as much cable through as possible. I have never had a problem since as the cables must have stretched enough to make it easy by hand. Curiously I have also never needed to tighten the cables with the adjusters, which suggests it might have been better to have set them with some adjustment in the first place.
Glad you managed to change your cables OK.