countdown timer schematic diagram
I'm sorry, but this is not a straight forward project. To accomplish this, you have to do a fair amount of experimenting and testing. The difficulty is that you need to interface with an unknown circuit. The keypad interface of the timer can use any one of a number of interface techniques. Likewise, the buzzer output could be a simple on/off, or a pulse, or a waveform. Until the interface is known, its hard to know what the exact circuit would look like.
You mentioned the timer is from Radio Shack. Some Radio Shack devices came with schematics or the schematic is sometimes available on the Internet. If you can point the forum to a schematic, we can be of more help.