Those small cartridges are gas charged, not liquid. What you are thinking could be done is -no where- near as easy as it sounds.
For instance, lets say you were using a liquid refrigerant (which is what liquid CO2 can be considered), something more normal though (ie, smaller working pressure) like R-134 (like you would see in a vehicle A/C system).
Here's an explanation of how an A/C system in a car works:
You would essentially need to replicate this, with your CPU cooling block replacing (poorly, unless designed right) the evaporator coil. If you notice in the diagram, there is a low and high side to the system. The low side is under fairly high pressure (approx 50 psi), while the high side is under even higher pressure (approx 200 psi) - note that the pressures will vary due to a variety of reasons; these are just very approximate values.
This isn't a system that can be easily built from scratch by someone in their garage; you certainly wouldn't use CO2 for the refrigerant, either, as it doesn't have the proper characteristics needed for such a use (there's a reason freon and later refrigerants were developed - and a reason ammonia gas was first used, though it is a nasty and poisonous refrigerant that, while it works very well and is still used in industrial refrigeration/cooling - it is not something you want to play with).
Any homemade system would incorporate a none-too-small compressor, plus all the attendant tubing (mostly copper or stainless steel line), fittings, heat exchangers, etc. You have probably seen a water-cooling setup for a PC; maybe you've even built one or installed one. An A/C system for a CPU, while more than possible (in fact, I think there have been one or two -expensive- kits available for extreme overclockers of PCs in the past), isn't something you easily homebrew; and what you end up with is going to be more bulky and potentially dangerous than any water cooling setup. Leaks will be more likely at the pressures being dealt with...
What you are saying can certainly be done; but unless you are an experienced A/C technician who wants to play around with such a system, or you know someone who is... Let's just say a little knowledge can be a dangerous thing in this situation. You're ultimately going to want someone you can go to with questions and help; you're going to want to do a ton of studying on the subject. You'll probably want to read about how both A/C units (houses and cars) are configured as well as refrigerators/freezers (the principles are the same, though). There is probably as much to learn as there is in electronics...
Once you get to the point where you can possibly think about building such a rig with confidence that it will work, you can expect to spend a lot of money doing it, unless you want to reconfigure an existing system (like a small window A/C unit or a small refrigerator); even there you are going to need equipment and other tools just to do the recharge after you break the system for the reconfiguring, not to mention the refrigerant (some refrigerants can only be purchased by licensed individuals, btw).
Good luck with your efforts!