Technically speaking you just need the votes in the House. Therefore you could be impeached if they dislike your tie. Yes it would be a ridiculous argument to make about how tie color & style rises to the level of high crimes & misdemeanors. However there is nothing that could stop them There is no provision for someone (like the USSC) standing up and saying ‘This is stupid!’. It would be the Senate’s job to do that in the trial.
Politicians are all about ridiculous arguments!