Anything below the 7 refresh template is, technically, not a wizard. But there are still some spellcaster options out there.
As rientelfon said, channeling and ritual would be the first option. You're either a focused practitioner or an apprentice that hasn't learned all that much yet and is limited in what he can do. You can later replace channeling with evocation and so on, once you have the necessary refresh.
You could also look into sponsored magic. Maybe your magic doesn't come from yourself but rather an outside source. Maybe the land you live on is a special place, so you only can cast spells inside the city limits. Or a powerful Sidhe Lady or one of the gods has granted you some powers, as long as you work for them.
Another option could be to link some powers to an item of power. Maybe you were injured in the war and now you can only ever cast spells when your staff is around. That could be an item of power worth +2 refresh that would allow you to drop the refresh cost down to 5 for the wizard template. But if you lose your staff, you're just a grumpy old guy that rambles a lot.
For your "brawler" character, maybe you can go another way altogether. Maybe he is so specialized that he only knows one or two spells of biomancy that allow him to transform himself a bit. You could say that your spells are giving you the strength of 10 men, and you just take inhuman strength and attach it to human form. Casting the spell would merely be the way you access the powers hiding behind "human form". You can, of course, add other powers to that as well, as long as they make sense to you and your GM.
