Dealing with pressurization?

I've been playing for a while and love the game, but as the ships keep getting bigger (I finally started unlocking gecko class stuff), I've been struggling to empty all of the air in a ship only using those control panels instead of cutting a wall or opening a door between rooms with and without air in them.

Is each ship a puzzle that can be safely emptied of air without having to do that, or is this the way I'm supposed to be doing it? I feel stupid and I'm not sure whether that's because I can't figure out how to cycle all the air out, or if it's because I'm trying too hard to treat this like a puzzle.