I have a verbal argument between two individuals in a public place (Walmart), where words were exchanged, and threats of bodily harm were made. Long story short, a wheelchair-bound individual was coming down the aisle and said excuse me, while motioning to get by. She stated that she's not very good at driving the motorized cart and didn't want to hit anyone, to which the other party said, "not my f'n problem." Argument ensues.

One party said she said that, the other said the opposite. There is a claim of "I'll shoot you"; however, the person who said that claims she said, "I shoot, I don't fight". No visible sign of a gun, nor was one found during subsequent follow-up. Officers determined that the wheelchair-bound individual made the statement (with the intent to cause alarm), based solely on the statements of the other party.

Wheel-chaired individual paints a different picture, and wants to press charges for assault via threats. Video surveillance is of no use, and an independent off-duty officer informs the responding officers that both parties are to blame, as they both were making threats.

Without any further evidence other than word against word, is this a prosecutable case?

Excellent question for your local prosecutor. You should ask him or her.