i think that transmitter is not suitable for your application. the thing is that it is on the frquency range of a normal radio FM band, so you might get triggered by music on the radio....i htink that you dont want that.
and i might suggest one idea! you can use a receiver and emitter from a remote control car. the transmitter is quite small(there are remote controlled cars that have just one button or 2) so you can use them. the receiver is usually small too.
or you can use a simple radio oscilator on a lower frequency and simple receiver, like one with 2-3 transistors. one push-open, push-closed and so on. .....
if yo want to use that transmitter you can generate an audio frequency and send it to the transmitter. as a receiver you can use a simple radio, a pocket one, wich i think that it is small enough. then use a tone detector at the output of the radio so you can only get triggered by the specific signal.
have you thought IR ? not such a good solution.....
what about ultrasounds, it is a good idea, maybe get the car opened by whiseling?