When I open a page in Safari on my iPhone the handoff icon pops up in the dock on my Mac. However clicking on the icon will open Safari. As I am using Safari Technology Preview as my default browser I would like to know if there is some hack that would enable me to use is as a "handoff browser".
This is indeed possible, but only if Safari Technology Preview is your default browser as set in System Preferences → General. If you use a different browser, then the Handoff will always use the original Safari.