Axe/sword combos are iffy for me as well. Generally people that have shown skill IRL with two weapons are using similar weapons. Two swords, sword + dagger, things like that. Swords and axes are pretty different in usage. If someone did both I would feel it's just to game the rules.
As far as accepting someone's conversion work it to me comes down on gut feeling. Organized standing armies like Gondor, Uruk Hai, Elves and a few others I just feel are more "right" using standard equipment. Rabble forces (Orcs, Wild Men) and militia (Rohan, Clansmen, maybe Harad?) I'm far more open to random weapon assignments. There are exceptions. For example if someone had some Osgiliath (sp?) Veterans I could see them using almost any weapon available to the Orcs they are holding back. Dwarves thematically could have sword, axe or hammer.
If someone wanted to give a couple of their Elves axes then the had better put in the effort to make them look as nice as possible.
I personally think the weapon rules could have been left out. Yes they add another dimension to the game but I have never seen such a factor in SBG for trying to game the system as these introduce. For some players it doesn't mean a thing but others such as myself and many on this board are in the game first for the theme and "questionable" weapon swaps to get as much advantage on the table just spoils the theme...