Multiple realities
(covers information from several alternate timelines)
A weapons specialist was someone whose area of expertise was weaponry.
In the alternate reality, Carol Marcus's skills as a weapons specialist were what gave her the assignment to open up one of the advanced long-range torpedoes, with assistance from Doctor Leonard McCoy. (Star Trek Into Darkness)
In 2365, Ensign Sonya Gomez protested that Geordi La Forge was an engineer, not a weapons specialist, when he went to fool the Pakleds. (TNG: "Samaritan Snare")
Both Brenner and Fields were identified as phaser specialists in the script for "Balance of Terror".