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If you like to take that safety precaution I would recommend a stainless steel cable strung low (close to the gunwale/deck) to which you could string your netting.
If you don't want to drill small holes thru your stanchions you should be able to figure a way to clamp the cable onto the up-rights.
You can always use a life-line lanyard hooked up to their PFD and your railing.