The game is actually pretty biased towards swords (there are many more potentially good swords consistently in the game than other weapon types). There are lots of axes in the Aleroth catacombs, but not many after that.

Warriors tend to have plenty of skill points to spare, especially relying on spell books for mage skills, so it wouldn't hurt to have two weapon expertise skills. By the time you can meet the requirements for the better axes, though, there should be plenty of swords around. I stashed the axes in a chest in Joram's house, and eventually used them to trade with, after finding better merchants.

Free skills, and spell books you can buy

At least in the disk version of the game, with one level in Sword Expertise or Augment Damage (the starting skills for the male warrior), if you save the game and reload you will have level 2 of these skills. This works for other class and gender combinations, as well, but they have to put the first skill point in each skill themselves.