It's much easier to use a wired doorbell push button with a wireless receiver using the LRA-EX1000 Extend a Chime.
However, with a little ingenuity, we can add a wireless push button to your current wired chime. To do this, we are going to use the ERA-UTDCR Long Range Wireless Door Chime Kit by Safeguard Supply.
The wireless push button we will use is the ERA-UTX. When triggered, this push button will cause the ERA-DCRX wireless receiver to chime. On the back of the ERA-DCRX is a c-form relay. We will use the section labeled "Relay"
Assuming you want to put this wireless push button on the front door, open the cover of your wired doorbell and remove the wire for the "front" door.