Depends on how well you shoot, and what the shot really looked like. If all I was given was a 30yrd full side view on the "shoulder mount" of a buck, I'd cut his head off. 100% confident that I could place that shot where it needs to be to bleed him out and/or drown him. Neck shots bleed like crazy, and even though there are thick muscles in the neck, it's thin enough that I've never not gotten a pass through (rare that my bows don't pass through any part of a deer though).
But you weren't wearing my underwear that morning. If you weren't confident that you could make the shot to cleanly kill the animal, then you made the right call.
As others have mentioned, don't concern yourself with the cape when hunting. If you damage the cape, your taxidermist can either fix it, or replace it. You're mounting the antlers and hoping the face/neck looks right, cape is just a covering.