Arial dagger is nice. But don't worry, if you find your rhythm with axe, you'll find it has different advantages.
For example, there's nothing in a dagger arsenal like the lag that pincer can provide.
You'll find yourself winning a lot of battles early on(rankwise) due to the offensive nature of axes.
I'm not sure of the skill set in terms of relation to strength.
You will not be severely handicapped. There are nice lighter axes. Remember, the heavier axes may yield more damage to opponent, BUT, the characters that can use those types of axes will not come close to defending like you.
The best thing about CF is finding out combos others haven't used, mastering it, and creating an environment that your opponents are not familiar to and subsequently pwning them.