If the fighter's character is built as a diplomatic character, sure, awesomesauce. I had diplomatic fighter characters, my system supports them. But if the fighter used Cha as his dump stat, allowing the fighter to shine during the negotiations is a bit unfair to the player who actually built a diplomatic character (who is, OTOH, not optimized for combat).
In a game without personal interaction skills, you don't "build a diplomatic character" so neither of these applies. You cannot build a diplomatic fighter, you can create a fighter and play him diplomatically. You will not find it unfair that you created a diplomatic character that was outshined, because you couldn't create him in the first place.
I agree that removing skills after characters were built would be unfair. But I assure you that was not the case. Everyone was told ahead of time, built their characters, and had a blast.
We found it fun to apply our own creativity to the situations instead of rolling diplomacy and search checks. To solve a sphinx's riddle with our own brain power rather than with an INT check. Your group may feel differently.
I have never had so many compliments on a one-shot. If there was one player that didn't enjoy himself, he did not speak up. If he is stewing somewhere talking behind my back to someone else, I can't do anything about that.