I think you might be jumping to conclusions. Tape would be pretty hard to swallow, especially for a duck young enough to get angel wing. It's not impossible, but getting stuck under a wing or to the bottom of a foot seems more likely.
If a duck were to swallow tape it likely would stay in the crop and be regurgitated within a few days. If it's small enough to make it to the gizzard and your duck has access to grit it should pass on its own, especially if it doesn't have much plastic in it.
But unless you see more evidence than that the tape can't be found I wouldn't do more than keep an eye on them. Watch for a loss of appetite or sluggish behavior. If you think you see something, offer a special treat like fresh peas (or thawed frozen peas). If the treat is ignored then you might have a problem.
But I'm not going to go into much detail about solutions because the problem seem to me to be speculative right now.