I actually only use a scalpel now - for killing, cutting off legs and neck, and opening to gut. I change blades out frequently, so I have a super, super sharp blade. The sharper the blade, the easier to make a humane cut, the less chance of the blade slipping and cutting YOU, and the easier the whole process goes. Of course, a scalpel isn't the be all end all, it's just what I have, and what I'm comfortable with, and I've got a LOAD of blades, along with the resource to get a LOT more whenever (havels.com).
One could do the same with a good sharp paring knife. Use what is comfortable for you. If it's a cleaver, by all means, go with it!
The biggest thing is take your time. Set aside a whole day for it, even though it's 3 birds. Keep this section of the board handy for quick reference and questions. Someone is always on that has great information, and everyone is willing to help out for even the smallest question. Most of us have butchered at least one bird, many of us have done countless numbers of them. There's a lot of different ways to get to the same product, no exact way for everyone, but with the loads of good information here, you're set to make it a good go of it.