I've been wanting to experiment with such a system anyway, and the end result might wind up being added to Hampture Mk.III as an upgrade. Basically the air pump circulates air from the enclosure through a series of algae water filled 2 litre soda bottles, where airstones dissolve the air into the water so the algae can remove the CO2 and replace it with oxygen. It's then forced into the next bottle where the process is repeated, and so on. I call it the Human Centipede principle of life support. Patent pending.
If this works as expected, that's one more tie with the surface I can sever, and only the power cord will remain. Eventually I'd like some kind of watertight battery pack I can drop into place; I'd keep one charging at home while the other is in use, and every day I'd go out and swap them, thus keeping Hampture supplied with power. This would be a fairly expensive solution however so for the time being, a permanent power umbilical to the surface is unavoidable.
I definitely plan to deploy Hampture Mk.III With the surface air pump first, so as not to keep you guys waiting, in case that was unclear. You'll have streaming video from inside the habitat for a week or two, and then I'll get to work on the algae bioreactor upgrade.