You should use an ATtiny85 . It has four digital outputs and two timers plus analog in a $2.00 8-pin ic. I don't know how to do the
15 minute timer but Nick Gammon does. He helped me with an ATtiny85 Project
You can find him at this link.
http://forum.arduino.cc/index.php?topic=149015.0
Post your question in PROGRAMMING. with the title "How do you make a 15 minute count-down timer with ATtiny85 ?"
Wait for some responses before trying to contact Nick. He doesn't like technical questions via personal message . He won't answer them. You can run the whole thing off a 9V battery probably (not sure about that but it sound reasonable). All you need is the ATtiny85 and a loud PIEZO buzzer. You could make it very small. Crossroads would be willing to build them for you. He has his own electronics company. His email address is cardinalflyer@comcast.net .