That idea was dead from the start. Sorry. First of all, lets start by calling this air pump what it is, an air compressor. You claim the air is really cold yet every single unit I've ever worked on gives off pretty hot air. By the time the air travels through the system which consists of check valves, solenoids, sieve canisters, storage canisters and a few filters the air cools down to a temp that is OK or comfortable enough to breath. However it is by far NOT COLD. Maybe the air rushing past your fingers or hand might feel cold but it's not. There is absolutely nothing in that system that cools anything yet alone the air. So at best the air is room temp. However it's not even that as the air compressor heats the air. Don't believe me? Touch the compressor after it's been running for 10 minutes. I've burned myself plenty on these units.
That's about as far as my memory can take me without some research. If I were to guess I would say those compressors give off anywhere from 30-40psi. Maybe 60 but I doubt it. So like DrMorbius said you would never reach acceptable flow rates regardless of the tubing. These units where not designed to give off straight air. They are designed to pressurize internal canisters that are to give off no more then 6 lpm over no more then 2 hours time. At that rate the internal canisters stay pressurized giving off oxygen. Where it gets the concentrated oxygen is another story
Go to Home Depot and buy the cheapest POS air compressor they have. What you have is cheaper then that and needs to be rebuilt every two years. Unless you like excessive noise and poor output.
Then, lets look at the noise factor. Are you going to run this compressor inside it's original shell? That pretty huge! If you plan to remove the compressor and run it next to your computer then you are looking at 100dB.
btw:
Level at which sustained exposure may result in hearing loss 90 - 95dB
The only give and take here is that you might have a unit that is much newer then the ones I used to work on. In that case, maybe lower the dB output but as far as I can see with my first google search the main schematic to these things hasn't changed.
Sorry Bro.