I actually don't think the minutiae would be that hard. For example the process of rigging the mechanics would most easily be done by bribing the arbitration firm, which for enough money or future business or whatever could certainly be done. People at this level, high end lawyers, will lie their balls off for huge profits, and is totally human. I think even working outside of the other teams including the one you are favoring would be easy. Make it a closed circuit between you, the commish, and the firm.
The problem is motive for me. What benefit does Bettman really get out of taking this risk to say send the pick to Arizona or Philly? If MacDavid goes to Philly a popular team continues to be popular, but only marginally more so. If he goes to Arizona, I mean I don't think that makes them hugely popular, they are still going to be one of the least valued teams in the league. It just seems like a huge risk for very little return for a guy like Bettman, particularly with the leagues current finances.