Re: I can think of one.
10 meters depth is double atmospheric pressure, 20 meters treble, etc. 40 meters for a deep dive is 5 bar, which is pretty high pressure. (for me anyway, it's enough to drive some pretty serious air tools. it's not high pressure like in the tank though) So, as mentioned, the breathing gear would be scuba gear that delivered lower than atmospheric pressure. The pressure in a pressurized space suit is about 1/3 atmospheric pressure, and they do breath pure oxygen at this pressure.
I'm wondering if you could have an elastic suit that compressed your chest cavity to 1/3 atmospheric pressure to provide the ambient pressure, probably that can be tightened and loosened in the airlock so it's possible to breath once the air pressure raises again.