Cut their heads off with what?
I use anything I have. I just root about until I find a number of knives. Anything will work as long as it is sharp. I prefer a knife that fits well in my hand, with a blade short enough to work with easily. A pairing knife works fine, or skinning knives, or a standard fixed blade belt knife/pocket knife. A folding pocket knife works well too (IF it is large enough), but way harder to clean.
After a find a few knives, I sharpen them... or make my son's sharpen them.
If you move the knife slowly, while feeling your way, while stretching out the neck, you can slide the blade between the bones. Not cutting the bones, and sliding between them, will keep your knife sharp for longer.
As to how to sharpen. We have used a number of different knife sharpeners over the years. I recommend that you find what you have, watch some you tube videos as to how to use it well... and use that.
Also... different metal sharpens differently and loses the edge faster/quicker depending.
I never pay attention to such... we have too many knives anyway, to remember what is what.... it is just something to remember when you notice that one of your knives dulls faster than another.
I do know that the knives I like to use lose their edge quickly. Often I want a new blade for each bird... especially if I do not slide the blade correctly and hit/cut bone.
Part of that also might be my arthritis. Super sharp = less force required.
Do you cut their throat first to bleed them out or just cut the whole head off for this purpose?
Depends on the day, and what I feel like.
If you slit their throat, but keep the head on, then they bleed out better.
But, if they are hung upside-down, and you just cut the entire head off, they do bleed out some, just not as much.
If you want super perfect pretty meat... bleed them first. Cut off the head after they are fully dead.
Would excellent poultry scissors be an option to kill and remove the head and allow the bleeding out?
Yes. I just don't do well with scissors... they require hand strength, I have arthritis. But, lots of people love kitchen shears. I do not think you could use the shears to just bleed out... but they would work great for cutting off the head.