I'm curious to the answers you get. I don't know of an vining zucchini. Perhaps the closest would be in the trailing marrow family--something like Table Dainty?
I've grown that (not my photo). I've also grown Tromboncino--which is actually C. Moschata eaten a few days after flowering (will mature into a butternut type squash if allowed to mature). I also have grown Tatume, which is C. Pepo and a vigorous viner--but more rounded squash that will mature into pumpkin looking things but we use them as immature summer squash. I've also grown Lemon squash--but that doesn't trail as much as it grows a central stalk that can be tied up.
I grow my summer squash on cattle panel trellis--so I'm always looking for vining summer squash/zukes but I haven't found much. In fact I'm crossing Lemon and Tatume this summer as the beginning of a breeding project looking to get some qualities of Lemon onto a Tatume growth habit.