Smallest wireless transmitter?

At 1 metre range you don't need a transmitter on the remote device.
Assuming you want to "see" a circuit open or closed all you need is a tuned coil to act as your "transmitter".
Your base receiver unit is actually a "grid-dip" device (now there's a term from the past`) which is tuned to the resonant frequency of the remote tuned circuit. When the tuned circuit is open there is no absorption of the base signal but when the tuned circuit is closed there is absorption.