Double-handed weapons

[StayPuft]

I would definitely say this is up to interpretation. However, I would lean towards thinking you have to immediately discard the extra weapon and cannot exchange it.

The reason I lean this way is because these are the cards the heroes are starting with at the beginning of the game. It is not during the hero turn. In fact, after dealing these initial cards, the zombie turn starts first. Since the rules state you cannot carry more than two weapons (or one double handed weapon which counts as two), I take this to mean you would therefore have to discard it. After all, my assumption is you cannot exchange until that part of the hero turn, but obviously you aren't allowed to just hold onto it until the hero turn.

But, again, that is just my thought on the matter. It is certainly up to interpretation.