As far as I'm aware there's no way to do that. In fact I posted a thread asking the exact same thing only a few hours before you did.
https://forums.garmin.com/showthread.php?340204-Privacy-settings-hide-maps-only-Is-it-possible
Hopefully there is something we've just both missed. Right now I push all my activities out to Endomondo and share from there (they have an option to hide maps which I have enabled for all new workouts), but once I get a Fenix 3 HR I'll be looking to cutting down on the number of services I use which means I'll probably be more eager to share the occasional thing straight from Garmin. If my start or end point is home, a friends home, or work, I'll definitely not want the map being shown but I may want other metrics shared.