All right, I am going to appeal to the wisdom of the internet before wasting any more money!
Where I think I went wrong (aside from not having really looked at things online first) was in using the word pump rather than inflator...
This or very similar is what the store that sold me my bike last summer mounted on the frame for me: the Blackburn AirStik. I did not buy any CO2 cartridges or an inflator at the time because my temperament is such that I could more easily envision myself doggedly but happily using a tiny pump rather than anxiously using up a cartridge of which I would only have one or two and which I might accidentally discharge in a squib-like manner!
This is what I bought today: Second Wind MTB Co2 Hybrid/Compact Hand Pump. It has a nice feature which is the CO2 cartridge in a little plastic frame that clamps onto the pump and is also attached with a velcro strap. It is much squatter and wider than the other one, so it will not fit into the plastic bracket that holds the current one to the bike. Neither will the plastic thing that holds the inflator to the pump
So: what do I want? A mini-inflator like this one that I put into my pocket or into a bento box or wherever else I can stow it, plus an extra cartridge? (Tiny little seat bag is already jammed full with tube, tire levers and multi-tool, there is certainly no way I can fit anything else in there!) Can such a thing be obtained with this appealing little plastic frame and velcro bit like the one I bought today, only in the right size, so I can attach it to the pump I already have? Or is there some homemade solution to the problem?
Or is the new one I have bought superior to the old, and should I (tediously) see if LBS can attach it to frame? (But they will be annoyed that I did not buy it from them rather than from other slightly-less-local LBS! I cannot buy another one just for etiquette/politeness!)
Thanks in advance for attention to this matter!