Well you could, and it sounds poetic! But it doesn't exactly sound equivalent, more figurative, you know?
Without just has a few meanings, the most common ones mean lacking something, or refraining from doing something. Outside doesn't share that meaning, so you can't really switch them around in that case. But when you mean 'not inside', outside and without both carry that meaning, so in that situation you can use either.
It's like... say trip and fall. In one sense they can mean the same kind of thing, if you mean having an accident where you're walking and you end up on the floor. But if you mean trip as in 'travel', then you can't say "I'm going on a fall" - that would be weird!
Not like this is a prime language resource or anything, but just to show you it's still used in some situations and not just old books:
Edit: this comment is about the old TTS.
TTS pronounces it something like ja e utanför which is not incorrect. Pronouncing är as e is characteristic of the Stockholm dialect so it is important to know. TTS messes up restaurangen though. The au is normally just pronunced as a u.