You have quite a few healing options:
- Use a Wound/Vitality system (a la Star Wars), where (a) low-level characters start with more hit points (Con + D&D hp), and (b) most injuries (the Vitality part) heal quickly without magic.
- Use a Defense bonus (again, a la Star Wars), so characters will get hit less often.
- Apply armor as DR not AC. (OK, not exactly a healing issue, but something to think about.)
- Allow Wizards & Sorcerers to cast healing spells (and whatever other spells you'd like them to have).
- Allow alchemical healing potions.
- Allow Healing skill (perhaps with the help of Knowledge[Nature]) to heal significant damage via healing herbs, etc.