Is there anything special about this hack? I’ve got several hack and coping saws, both with fine teeth. What do you do about the bleeding? It seems that the hack saw would be too long for such a small place.
Also, you mention stress. I definitely don't want to cause my good boy to have a reason to hate me.
I like to use a unit like shown below. I sit down with rooster laying on his side facing right with both legs restrained by left hand and his body by my left forearm. I am right dominant so use that to hold saw. The bleeding is generally minimal and never life threatening. The bleeding may be good to flush out fines produced by whatever cutting tool is used. This not optimal time of year with mature birds in molt. They are less happy with handling and you can damage some of the new feathers coming in.
The whole process is more fun if you have a helper. For me it is just a small kid that helps me manage cutting tool after I get bird situated. Then I can focus more on getting the bird in a comfortable yet restrained position. Ideally, even when doing more than one bird everyone needs to be comfortable.
I have been cleaning cutting site and tool before cutting using isopropyl alcohol. Definitely do so if doing more than one bird. Process is more invasive than doing something like trimming horse hooves.