For anyone who is curious that may be reading this in the future:
*Puzzle Spoilers*
You grab the (depleted) oxygen mask in Mars in the area right before going into the reactor, but you have to fill it with oxygen in the Norad timezone. So you jump to Norad and to your right will be a gas canister you have pull out the sleeping gas into your inventory, and then you can attach your Oxygen mask to it instead and fill it with Oxygen.
Then you should be able to keep the Oxygen Mask on during the Mars airlock sequences and maze, and also the whole time you are wandering around Norad VI.
*End Spoilers*