And what makes you think it's a gun? Very well could be the Strap and end to Mjolnir, or a billy club, it's way to dark of a picture to tell.
Who say Don wouldn't carry a gun? Many doctors carry weapons, just because you don't see a gun doesn't mean they don't have one.
Look in the back of CW1 Director's cut, there's mention of a Col. Blake of SHIELD that walks up to Cap saying something like, "Nice seeing you again Cap." and cap doesn't recall ever meeting the man.
I'm only repeating what I've heard that's there from several people, I don't have the actual book.