No, you can't change the left mouse button to the F7 functional key. The software doesn't even allow to change anything. I tried to obtain information from WiKi, but nothing is available. Most likely, the Double-Clicker was developed to be used for a certain service/website.
You can try other applications like X-Mouse Button Control or HydraMouse.
These two apps are powerful when it comes to mouse button assigning and customization.