Looking at this again, it looks like it gets a bonus for unopposed, rather than for non-opener. And to confuse things more, it's the same message unopposed whether you have a garotte or not. (may be worth testing if it does different damage)
EDIT: Thanks for checking GoldS. Glad I kept those messages separate.
opener, opposed, barehanded:
You deal 2 stealth damage attempting to garotte the lake serpent.
nonopener, opposed:
You deal 2 stealth damage attempting to garotte the thug.
nonopener, unopposed, barehanded:
You slip behind the guard and garotte him for 15 stealth damage.
opener, opposed, with wire:
You bear down on the thug with your garotte for 5 stealth damage.
nonopener, opposed, with wire:
You bear down on the guard with your garotte for 5 stealth damage.
nonopener, unopposed, with wire:
You slip behind the thug and garotte him for 22 stealth damage.
opener, opposed, with lace:
You garotte the guard with a length of lace for 11 stealth damage.
nonopener, opposed, with lace:
You garotte the lake serpent with a length of lace for 6 stealth damage.
nonopener, unopposed, with lace:
You slip behind the thug and garotte him with a length of lace for 17 stealth damage.