How can I tell if option 1 will work?
Because the inner technical detail of dimmers, eg circuit diagram, is not normally published info, I think it will be difficult to establish which dimmer is suitable without buying one and taking it apart!
Unless you can find info on the web on which trailing edge dimmers can be hacked, the only way ahead would be to buy one that 'clicks' when you turn it off, take the cover off and check if one of the terminals goes directly to the rotary (or push) switch connections. If it does, solder a wire to the other switch connection (for the mirror) and try it.
If it doesn't, sadly no use for your bathroom. You have an extra dimmer in your spares box.
In it's modified state you would need to make sure your live feed is to the terminal you first identified as going to the switch.
For safety and liability reasons I would strongly recommend option 2!
PS if you are thinking of asking a sparky to do the option 1 modification for you, they won't - for the above reason.