You will be able to update the 172 without a working screen, the factory reset at the end of the update process isn’t strictly necessary, so just delete and re-save any iRadio presets afterwards.
There is a method for carrying out the factory reset from the front panel - if you wish to do it, let me know & I’ll refresh my memory!
Bear in mind that a factory reset will lose any wifi credentials & those won’t be easy to input without a working screen.
Regards
Neil.