I usually trellis cucumbers and just keep wrapping any stray vines back onto the trellis. I only prune overlapping vines IF airflow/circulation seems inadequate as in solid wall or fence with a netting trellis, but usually I grow cukes on a free standing trellis.
But last year, I let a volunteer cucurbit grow which turned out to be cucumber, and since the trellis above it was reserved for melons, I let the cucumber take off along the ground to see what would happen. It turned out that cucumbers root from leaf nodes just like winter squash, and with the additional nutrients and water, the leaves and vines grow HUGE with multiple branch vines. When the cucumber swallowed up 4 feet of a 2ft wide row, then proceeded to swallow a pepper plant, I had to out a stop to it and I turned back most of the vines but ruthlessly cut off vines that were reaching for the pepper plant, too.