Are you saying you'd rather have a handgun at long range than say a rifle? I'll agree that at any range, a handgun is better than nothing, but at such extreme distances, a handgun is practically useless for defensive purposes. If I were in the situation outlined by the OP, certainly, I'd do everything I could do, but I'm a realist. There's practically no way I will win this fight.
I would venture that most of us do not walk around daily with a rifle. Often we do have a handgun with us.
125 yards in not an "extreme distance" for many handgun shooters.
All that it takes is one well aimed shot; even in a "defensive purpose".
I would take a moment to consider mindset.
To paraphrase an old saying, "I am the weapon, my gun is a tool. Or is it I am a tool and my gun is the weapon." It almost always comes down to the person behind the trigger, not as much as what "hardware" is connected to the trigger.
Sure, most rifles are easier to hit your target with at 125 yards than most handguns, but that does not mean that one can not easily hit a target at 125 yards with a handgun; unless you do not have the skill set to do so or are physically unable to do so.
Don't be surprised if when you argue for your limitations, that they are granted.