Yes, you can use the E6 radio control transmitter (from the TinyHawk RTF) with the TinyHawk Freestyle. You will just need to use Betaflight Configurator 10.5.1 (https://github.com/betaflight/betaflight-configurator/releases/tag/10.5.1) and copy-paste the CLI settings from here:
https://drive.google.com/file/d/19YU-7_lTTVPoGIpic9HPO6FQ93-d8DXs/view?usp=sharing
However, if you are using an older E6 transmitter and are having issue binding with your Freestyle, please re-flash the AIO Board with the custom firmware here:
https://drive.google.com/open?id=11CQuCRVWm4M1mfFDTqCbBhsPkSyOILmd
Then, apply the CLI settings from here:
https://drive.google.com/file/d/19YU-7_lTTVPoGIpic9HPO6FQ93-d8DXs/view?usp=sharing