"Military" might imply a tool for political work, that is, centralized and controlled adjusting of national borders or the attitudes of neighboring nations. We don't really see anything political in the combat actions of the TNG Ferengi. They just steal stuff, and blow up other stuff that stands in the way of a good theft.
It seems unlikely that Ferengi combat vessels are in any way "military". They might sell their combat services to the highest bidder (say, the Grand Nagus) in a mercenary manner, but as you point out, the history from "The Magnificent Ferengi" suggests they don't.
Except you can use military force to achieve a financial end. India was originally colonized by the British East India Company, a private company rather then a government, its only later that the British Crown took India away from the British East India Company.
Or look at Opium Wars, those wars were not about conquering China, but forcing China into a bad treaty where they would be forced to expand the opium trade in China.
So it seems a bit silly for the Ferengi not to have a military, it seems like those are kind of rotten things you would expect from a society that is ultra capitalist and has no moral restrictions on doing business. Why wouldn't the Ferengi act like a 19th century colonial power that mixed military with business?
A rather good defense against gunboat diplomacy is to hail the gunboat and tell the skipper that his payment for the engines is two days overdue... And the small print in the contract allows a better-paying customer (both the Klingons and the Breen are lining up) to come confiscate the engines unless suitable amends are made.
Except that wouldn't work if they are dealing with power that they don't have a business connection. If Federation Starships were harassed by random hostile aliens, doesn't make sense other civilizations would be attacked as well?