Based on my memory, I think this worked well in JA2. You could miss at point-blank range, but it was relatively rare even if you aimed at the lowest accuracy setting.
I did a quick test in JA2 to try to judge what the average hit chance is in that scenario. I created this setup:
Early fight in the game; attacking first Drassen sector.
Fox positioned next to an enemy. Her accuracy is 69%. Using her starting G17 pistol.
I made sure to not get the "aiming at same opponent after one shot" to try to get the same accuracy for each shot.
I did modifications to the source code to show hit chance (the game calculates a hit chance based on many variables and factors with a percentage ending up between 1 and 99), and to make damage always be zero and gave her infinite AP to make the test go faster.
I kept doing shots with lowest aim level and hit chance was 68% -> 75% throughout the test (I forgot an obvious factor which is that her accuracy would go up the more I shot, so it didn't end up being static).
Results:
100 shots
81 hits
19 misses
So, in that scenario, a weak character with a starting gun ended up having a practical hit chance of about 80%.
By the way -- for anyone who's curious about how this all works -- because of how the bullet simulation works the practical hit chance is higher than the hit chance the game calculates (I wonder if that was one of the reasons they decided to keep it hidden from the player):
The game calculates the hit chance. Let's say it became 75%.
The game "rolls" a number between 1 and 99. If it rolls a number equal or lower than hit chance, it's a hit. If it's above, it's a miss. Let's say the game rolled a 80 (miss).
If we hit, the bullet trajectory will match perfectly where we're aiming. But the more we miss (aka, the difference between hit chance and the number rolled), the more the bullet trajectory angle will divert. But since the bullet path is fully simulated, a "miss" can actually turn into a hit if the shooter is close enough to the target and if the angle diversion is small enough.
If you guys do end up with allowing misses at point-blank range, I hope you don't end up doing the same mistake as the nuXCOM games where it looks visually ridiculous. In those games, you'll see the soldier hold up a gun literally on an alien when you're right next to one, which makes the firing animation when missing just look absurd.
One thing I enjoyed about JA2 is that what you see visually matches up what's happening. You can very clearly see the paths bullets take. That's something that bugged me about the nuXCOM game where the bullets you saw visually were just pure cosmetics.