I searched for CO2 and did not find any matches – so please let me describe a cut-out method that may be new to you.
If you can create an enclosure, or if the hive is already in one – where you have access to the bottom, this works.
Use clear plastic bags or sheeting to complete the enclosure so that it is generally air tight, and use plastic bags under the bees to catch them as they fall from the comb. Use a plastic tube attached to a CO2 tank – the kind of tank that is used to push beer up from a keg on the floor to the spigot at a bar – and direct that stream of CO2 to the surface of the comb, and up between the comb layers – and the bees fall right off/out and onto your prepared clean plastic surface under them. Use multiple layers of plastic, so you can lift one off and have more below for the next batch of bees to be gassed. Net, bag and gas into their bag, any that are flying about. Use a low volume gas flow so that you do not freeze the regulator or hose.
Move the motionless bees quickly to their new hive, spreading them across the bottom board (screened if possible) – as they are now overheating due to their metabolism and lack of fanning/breathing. Use a hand fan on them to get air back to them in their new hive. Once the bees are off of their comb, it can be harvested or framed using the rubber bands / cotton string method.
This method works remarkably well where the bees are in an enclosed spot that is hard to access. You obtain all of the live bees, plus as much of the original comb as you can gain access to.
The plastic should be clear so as to permit you to see as much as possible as you work. The enclosure does not need to be truly air-tight, just tight enough to allow it to fill with the CO2 long enough to knock them out.
Have used this method where (1) the bees were outside – under the eve of a house. A vacuum would also work in this case. (2) In a tree that I was not allowed to cut down (so I made one access cut below the combs and used an L shaped knife that I crafted to go after the comb.) and (3) Where the bees were underground within a tomb that contained urns of ashes and I had but a small opening into which I could reach.
A caveat – all of mine were cerana, but I can not think of a reason it wouldn’t work with mellifera.