She's never had a reason to carry around a gun. In the original trilogy, her wire-fu abilities made sure she didn't need to. I suspect in DOFP, from the set pics that we've seen of her with a gun, she'll probably just take someone's weapon, through good ole' fashioned ass kicking:
"She's good."
"You have no idea."
And Bryan would find a way for her to quickly get rid of it.
Besides the times, in FC particular, that she's worn clothes in her blue-scaled form (in the CIA meeting with Old Stryker where she wears that black trench coat jacket and during the final battle on the beach where she's wearing her blue and yellow uniform) it didn't make sense that those two wardrobes would *also* morph. When she transformed into Old Stryker, "Stryker" should also have on the women's black leather trench coat and when she transformed into Shaw, "Shaw" should also have on Mystique's cleavaged-blue and yellow X-men costume. Such lazy and inconsistent writing/directing.