I use a filet knife for the jugular-slicing part. The blade is about 6" long. I tried a small-bladed knife at first and had trouble accurately making the cut through the dense neck feathers on the cockerels. 6" is overkill for knife length, but that filet knife is the sharpest knife I own and it works.
The actual cut doesn't hurt when the knife is truly sharp. Yes, I did learn this the hard way. The cut does start to hurt several seconds later. Accidentally cutting myself with the knife and not hurting made me feel a little better about the slaughter process. If the knife is sharp, the bird is hydrated, and the initial cut is done properly the bird should be expired before any pain has a chance to set in.
I use a different knife for butchering so I don't accidentally ruin the edge of the slaughter knife. But I mostly use poultry shears. A good pair of poultry shears will make the process a whole lot easier.