A phone call to someone may be in order to avoid last minute problems.
From reading passenger anecdotes around the web, it seems apparent that enforcement of (or understanding of) the rules is not the same everywhere. Any item that is slightly questionable may be perfectly acceptable to one screener in one airport, while another screener at a different airport might find fault with it.

So for items that are not clearly defined in their rule book (and I have to believe Scottish cap badges are not clearly identified), it might be better to check it in luggage and avoid the risk. Because once you're at the checkpoint, saying "they told me on the phone it was OK" isn't going to impress them very much.