Try it with the bell push held to the fram with tape before you drill any holes. Might work if the reciever unit is just going indoors by the door.
I used a Byron wireless door bell because I was concerned the metal foil covered insulation in my walls would cause problems with the signal. Our mobile signal is certainly affected.
The set up I have uses an ordinary wired push button on the outside with a short wire through the wall to one of these "wired push converter" on the inside. Basically it's one of their wireless door pushes without a button on it....
http://www.chbyron.com/Byron/Wiredpushconverter/68/68/90/45/model/p/294/SX32/That can be used with any of their SX series of receivers/bell boxes. We opted for a battery powered unit that and can be moved around the house. They also have mains plug in units.
http://www.chbyron.com/Byron/DoorChimes/68/68/90/45/model