Well, I had a pending email in to Perfectflite. Options are a bit interesting for small spaces. Being inside the coupler of a 2.5" OD rocket does not give much space. When I asked the same info of Perfectflite, this was his response
"The A23 will run the altimeter just fine. The altimeter has a very low current drain, so an A23 will run it for a relatively long time (10 - 20 hours), BUT the A23 has limited ability to provide a high current "surge" to fire the ematch. A good quality, fresh A23 will run the altimeter and fire a single (at a time) low current ematch but generally will not fire two redundant matches connected in parallel. As long as you are using one ematch for each channel (drogue and main) and since they will not be firing at the same time, it should work.
If you use an off-brand A23, or one with a "use by" date that is coming up soon, you could have a problem. Also -- the ematches that you provided a link to are Chinese -- the quality and consistency may be variable, and the exact firing current isn't specd by the seller. You should ground test them with the A23 brand that you plan to use before flight. If you can connect two in parallel to one of the altimeter's outputs (drogue or main) and the altimeter will fire two at once during testing, you should be OK to use a single match on each channel in flight.
(Unless the single match that you use during your flight happens to be defective -- that's why using a more powerful battery that can fire several at once, and using the two in parallel for the actual flight, is a better idea. But you won't be able to do this with the A23.)
Those ematches are cheap -- do a bunch of ground testing before you decide on whether your matches and battery are OK. Those ematches are cheap, failed deployment isn't....
If you have the USB data download kit, you can do some vacuum ground tests with a shop vac (described in the altimeter manual) and then download the data and look at the voltage plot. If the battery voltage drops a bit while the ematches are firing, and recovers quickly, that is a good sign. If the battery voltage drops by several volts or more, and doesn't recover to near-original levels after firing, then that's showing a sign that the battery isn't really up to the job.
Also -- common "N" cell holders don't really fit the A23 properly, so if you are using this kind of holder make sure you tape it in or it may pop out during flight (not good).
If you can somehow cobble together a reliable way of holding 2 or 3 "CR2" lithium cells in series, that would be a better bet, able to provide more current. You may be able to force two of them into a single "AA" battery holder if the holder is somewhat flexible. If it doesn't seem robust, don't fly it....
We have a 2 cell LiPo battery that is about the size of an A23 and is rechargeable and can supply more current than the A23, but the charger is not yet in production so that won't help you right now if you are in a hurry."
Not the worst news, but not sure I want to rest the fate of my rocket on the battery. I may do some testing with a Lithium A23 just to see the ground results. The 9v is not impossible, just a little snugger than I'd prefer. More info in a few hours.