Wouldn't you need a pump if you're conserving air? If the pump moves the air back into the habitat, sure you could repressurize the airlock by just letting the habitat's air flow into it.
I would expect air (and water) to be conserved because it's going to cost to replace them, so yes, pump out the airlock before opening the door.
This is just as to how the details of a spaceship airlock would work in an SF novel.
How big is the spaceship?
From a practical point of view, don't make the airlock any bigger than it has to be, because the bigger it is, the longer the pumping out process is going to take, and the more energy it will use. If the ship has one airlock then size is going to be a compromise between making it as small as practical whilst large enough for any likely task. If there's more than one, then you might have different sizes - something small for a one-person excursion, something bigger for a group to exit, or move machinery out through.
From a safety point of view, the time spent doing the pumping out is also when your user can check that the suit is functioning properly and not leaking.
From a boredom point of view (and if you went to get really technical), your spaceman might need to be patient. Pumping air out of an airlock takes time. With current tech (OK, article is about 8 years old) you could be looking at 10 minutes plus, with the possibility of hours of prep time adjusting to a different atmospheric mix akin to diving.
This answer seems to indicate the air-lock pressurization/de-pressurization is a drawn out process. Pressurisation is said to consume 45minutes (somewhat less in case of an emergency). Depressurisa...
space.stackexchange.com
The NASA/ISS checklist document linked in that article (International Space Station ISS EVA Systems Checklist) runs to in excess of 600 pages.
and another one referencing an incident on the ISS where the EVA team wanted back in in a hurry. Start to finish, about half an hour, with eight minutes taken to re-pressurise the airlock.
I just saw a show that featured an incident in which an astronaut on a spacewalk to install the Canada 2 arm on the ISS was temporarily blinded by contaminated water inside his helmet. His colleague
space.stackexchange.com