I can't (yet) speak to Shishkebab nor That Gun, and in fact this is a speculative answer altogether. However, using the Vault, my hunch is that the following weapons will qualify:
- .357 magnum revolver
- .44 magnum revolver
- Hunting revolver
- That Gun (confirmed)
- Anti-materiel rifle (Unconfirmed)
- Lever-action shotgun
- Combat knife
If I had to guess, I'd think that the Shishkebob would not qualify, as it seems too long-bladed to be a knife. That Gun, on the other hand, I'm up in the air about -- seeing the artwork I could go either way on it.
I will update this answer with The Truth ... Once enough details are known that said Truth can be fully ascertained. :) It may be a few weeks before the Vault is populated well-enough to do so. Among other things, it feels like at least one or two of the rifle types should qualify, but none of the artwork looks lever-action.