Because I want to collect the blood, I think I will just try to act really quickly and get it into the cone.
It sounds like you are expecting more blood than you will actually get. But after the first time, you will know how much there really is (or isn't.)
I usually hold the shanks and the wingtip feathers in one hand while I chop the head off with a hatchet in the other hand. After that, I deal with the flapping headless chicken in a variety of ways.
If I want the blood in a particular place I just point the headless chicken in the right direction while continuing to hold on tight. (Chopping block right next to the compost pile would work fine.)
If I don't want to stand and hold it, turning it loose is one option. This was the first method I learned, and I don't remember seeing any bruising, but I got tired of picking chickens out of mud puddles (because they always seemed to go downhill, and of course downhill is where the mud puddle forms.) So I don't do this anymore.
On a few occasions, I butchered chickens while there was knee-deep snow. I could stomp a hole in the snow, cut off the chicken's head, and stick the chicken into the snow. Very tidy, but butchering in cold weather makes for some pretty cold fingers!
Sometimes I put the chicken under an upside-down bucket: chop the head, put the chicken under the bucket, and put a foot on the bucket to make sure it stays put.
I've never noticed bruising from any of these methods.
The one method I will not repeat: hanging the chicken from a tree by its feet. That let the headless chicken flap around up in the air spraying blood, and it made a much bigger mess than any other method I've tried (yes, more mess than turning it loose.)
I know cones work well for some people, but because I learned other methods first, I never bothered trying a cone. So I cannot say how my methods compare with a cone.