even tho it does not look as if it is in pain im sure any fowl having its beak or bill ripped off by a coon is in pain it will be the best for her but she is your pet so i can not tell you what to do but if it was mean i would
I have a crossbeaked silkie hen named Felicity (thought it was male at first used to be Felix), and I have to hand feed her everyday its alot of work but w/o a beak I don't know if the duck would want to live like that.
Give it some time before you cull. Watch how it eats. It's very likely that it will adapt and be just fine, but if it is unable to care for itself you should put it down. If you're willing to dedicate a lot of time to it, you could easily keep it living happily by hand feeding it every day. Put some neosporin on the beak to prevent infection and watch her carefully. Examine the bird daily and check for weight loss and if there is anything in the crop to see if she's eating. I'd give her a week before you decide to cull.
I guess ducks do that dabbling thing... without the bill that would be difficult. I'd still give it a day or two just to see. There's always a chance. Tomorrow, if the crop is full, it's eating on it's own.