Learn English – “Except for” vs. “except on”

• Fortunately, apart from a broken toe, she was not badly hurt after the car accident.
  -- while apart itself is acceptable, it is awkward in this particular example.
• Fortunately, except (for) a broken toe, she was not badly hurt after the car accident.
  -- best option that conveys the meaning appropriately in the context.
• Fortunately, other than a broken toe, she was not badly hurt after the car accident.
  -- fine; can be an alternative to except, which is the right word in this case.
• Fortunately, besides a broken toe, she was not badly hurt after the car accident.
  -- inappropriate: avoid besides when showing an exception.

Except is used when some member/s of a set, stated or implied, are excluded for some reason:

all the whole numbers except multiples of 10

all the class except Ann

all birds except penguins

all factors that would affect him ('everything') except the weather.

Without (in the fairly closely related sense) means unaccompanied by / not possessing (usually something one might guess might possibly be present):

all the class (members) without packed lunches

all birds without flippers.

So 'except' (or but or bar) is appropriate here, not 'without' (which is often replaceable by 'lacking').