Cripple X:
Alternatively you could just have magic be a trapping of regular skill use, e.g. An Athletics roll could described as using a Jump spell. All that would really require is a Aspect with a Permission.
This is the approach I prefer, in my slight dabblings with D&D-inspired Fate/SotC. The magic becomes how the character represents their skills. If they have a good Shoot skill, it's because they're slinging
magic missiles. Good Stealth or Deceive means that they practice invisibility or illusion magic. Etc.
Aspects and stunts would make the use of these skills more magical, in how they're applicable and limited. The wizard would, for instance, be able to hide without necessarily having cover, but injury or other deleterious circumstances might hinder the wizard where they wouldn't hinder the thief.
One might call for the use of fate points for particularly magical effects, which I think would emulate the traditional disadvantages of a wizard. Consequences are a fine way to stock up fate points, so a wizard might gladly forego a high Physique. A particularly bad Trouble aspect (or other aspects for that matter) such as "Not my precious spellbook!" would pull the wizard in different directions and help them rake in fate points, to be used for a string of mighty spell castings later.
Just my thoughts. I haven't tried many of them in practice yet.