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.

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).