There really isn't such a thing as "optimisation" in 2e. Stats are not nearly as important as picking your fights wisely, and level bonuses (i.e., THAC0 improvements) and magic gear (even a very little bit) will quickly swamp the minor difference between a STR 9 fighter and a STR 18/00 fighter. There's not as much "keeping up" with each other either, because the niches are not as distinct and there is much, much less party synergy to try to maintain your usefulness within.
One can theoretically try to get a lot of bonuses and be extra-good at combat, but that's not optimisation in 2e parlance, that's "powergaming". It's not very useful, satisfying, or well-regarded. There's not much point to doing it, because the game simply isn't designed with balance as a primary system purpose. And that means that the contrary, suboptimisation, doesn't really exist. That's just called "normal play", in opposition to "powergaming". The power curve is not nearly so steep, and it's not so necessary to keep slavishly on-target to the power curve to enjoy the game and be effective.
So yeah, low-strength fighter is mechanically viable, in keeping-up-with-the-party terms, simply because that's easy to do without trying. D&D's history is chock full of STR 9 fighters, and until 3e came around, nobody really considered such a low strength a disability in a fighter. It was just one variation on the typical fighter.
The concept of being incompetent at being a fighter, though, is not really something the system supports – if there's no real "optimisation", you can't really be suboptimal, right?
So, you have to approach it differently than you would in, say 3rd or 4th edition. (After all, AD&D 2nd edition is a different game.) There's no system support for poor performance, so to make a fighter who's incompetent at being a fighter, you have to play them incompetently. The difference between a good 2e fighter and a bad 2e fighter isn't as much their build, it's the choices they make during play. (This is generally true of D&D prior to 3rd: it's not how you build the character, it's how you play it.)
To be incompetent at fighting... just be not competent at fighting. Make poor tactical choices. Charge into the fray at the wrong time, then change your mind, leaving yourself exposed in a bad position. Use a frontal assault when flanking and surprise are better, and vice versa. Take action unilaterally when group coordination would be better, and vice versa. With that "quite a mouth on him", you can easily get him into trouble that's a bad idea (the opposite of the "choose fights wisely" that I mentioned above), and that's pretty suboptimal all by itself. Since "optimisation" in 2e lies in your during-play choices instead of your build, to be suboptimal, just make suboptimal during-play choices.
So yes, the concept is actually highly viable, but you're going to have to completely unlearn how to accomplish it in this new system that merely looks familiar, but under the hood functions completely differently than WotC-produced D&D does.