It sounds to me like the two red wires have some sort of alternating current signal, perhaps superimposed on a direct current "bias" that may be deliberate or inadvertent, when the alarm is sounding. The piezo transducer will not operate on direct current (but a small DC bias won't hurt it either), so the CB must also contain some sort of oscillator to make the piezo produce sound during an alarm condition. If the reed switch is normally open, and is held closed by the external magnet (the long white plastic thingy), the switch is NOT in series with this oscillator and the piezo disk.
I would have designed it so the reed switch, when it opens, turns on the oscillator and that directly excites the piezo disk. This is a little more difficult to design because you need to sense when a normally closed switch opens. That requires a small current pass through the closed switch at all times, which will limit the battery life unless the current is very, very, small. So, the absence of that small current "triggers" the oscillator to turn on and sound the alarm when the reed switch opens. You are able to "light" an LED with this signal because (1) the current source is small and (2) the LED acting as a diode rectifies the AC signal that was applied to the piezo disk.
So, if you don't need the audible alarm function (or if you can provide it in some other remote location), hack the CB to find the reed switch and cut the traces to the rest of the circuit to isolate the reed switch terminals. Solder two insulated wires to the reed switch terminals and thread them outside the case to your external batteries, fan, etc. No need to use the button cells or the CB inside the case for anything.
You said there was also a magnet inside the case. That is unusual for a consumer product. Usually there is only a single external magnet (the long plastic object you secure to the window sash) that holds the reed switch closed until it is physically separated from the switch by raising the window. Commercial alarms often have a "bias" magnet inside the case that works in conjunction with the external magnet as an anti-tamper device to prevent someone from defeating the sensor by simply bringing a strong magnet nearby. Can you provide a picture of where the internal magnet on your sensor is located with respect to the reed switch? If this has an anti-tamper feature for one dollar, I would like to know where to get one!
