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are boyz allowed to have a shoota (NOT a big shoota) in one hand, and axe/choppa in the other?
Not for rules purposes. For modeling purposes yes, but I would assume they would play as slugga/choppa boyz
Wash: This landing is gonna get pretty interesting.
Mal: Define "interesting".
Wash: [deadpan] Oh God, oh God, we're all going to die?
If you have the pieces to do it, you can have them holding the Slugga Choppa, and sling then Shoota, or vis-versa. It makes them interchangable depending on who you are fighting. But yeah, in game mode, they can only use one or the other PER GAME, not per turn. Decide at the beginning and keep it that way.