This is by far, no doubt, the absolute worst part of chickeneering.
We had her in the cone twice and could not do it.  Big Burly Manly Man With Chest Hair And Power Tools, complete in steel-toe boots and flannel shirt, started crying and couldn't swing the blade.  I couldn't even look.
We made some calls and found someone at a semi-local feed store (a lady we have done business with before and whom we trust), who was kind enough to say she would humanely dispatch them for us for a small donation. 
I feel like a dirtball right now.  I have to work this afternoon, so hubby took the girls out to the feed store to have them humanely taken care of.  I said my goodbyes and cried like a blubbering idiot.  Martha has been sick for so long, and we really should have culled her a few months ago but wanted to keep trying to cure her infections.  With her, this isn't unexpected & I didn't have *as* hard of a time saying goodbye to her.   Rhoda, though... this just showed up out of nowhere & we don't know what even happened.  She just started limping one day, and it's just gotten progressively worse & feels like a dislocated hip & we can't help her.  She cries.  It's awful to see, and she's an otherwise really healthy, robust, GORGEOUS Rhode Island red.  She still eats and steals food from the other chooks, but she's in such obvious pain.  That cry is terrible to hear, even harder to watch her walk. 
I just hope it'll be over soon.
I love all you guys... you're the best.