The basic design of this module uses the BT signaling to do the PTT function, so it isn't something you could do completely with this design. Having said that, the KC Wireless module will stream bidirectional audio once it is connected and the PTT is not enabled (which is how the most recent firmware comes up..). That will still give you audio in and out of your radio. Adding another wireless switch module that could control the PTT of the radio would be sufficient to give you a way to control the transmit function. That would be in addition to this module. I expect there is an Instructable article that would have something you could possibly use. I would also take a look at Amazon or Ali..
I have used this for a wireless mic before, so it could work for your setup. The only caveat is if your headset will work with the PTT function properly.
Bluetooth Gateway Module fo...View Instructable »