Knit fabrics are your best bet, e.g. old pantyhose/tights, old t-shirts, etc that are securely tied to the trellis. Flexible and wont dig into the fruit, but will support a decent amount of weight. Many forms of stretchy-net-knit fabric will work out.

You can harvest obvious cucumbers (tube shaped fruits) fairly young if you notice them, let the others go until fully ripe late summer/fall. Honey nut squash can also be used as summer squash, fwiw, if you identify them and harvest them early (they tend to bulb at the bottom long before ripening).

Since honey nut squash, pumpkins and cucumbers are actually members of separate species within a genus, there's relatively low chance of them crossing (unless some close neighbors grew other varieties of one of those species), so if you have random clues from previous batches, there's a good chance they'll hold for newer ones.