OK so we are looking at the remote being quite small especial if you want 4 buttons on it. There are quite a few key fobs out there which are designed for the hobbies market that we can use for this.
The receivers from Adafruit like these http://www.adafruit.com/products/1096
4 units at $4.95
Using a remote control like this http://www.adafruit.com/products/1095
The electronics and firmware are not too difficult to create most of it already done by the Adafruit remote and receivers but the mechanics of moving a rod 3 inches with a reasonable amount of power to move a book etc are more challenging.
I will do a bit more fishing for you.
What is your budget/timescale for this. Feel free to send me a PM if you dont want this public.