I have done both. With the viper with the infected gum, I pinned it between two pieces of foam and used a cleaned probe to open the mouth and tweezers to remove the fang. I then rinsed it out while it was still pinned and once done, I used a hook to transport it back to the cage. My fingers never touched her the whole time because there was no need for that. As for the cobras, I had to force feed them when I first got them. I used hemostats to pick up a tube. I cracked the cage door to allow the tube to go in and coaxed the cobra into the tube. Once it was in the tube, I grabbed the body of the snake to prevent it from slipping out. The snake was properly restrained and even though I was holding it, it was physically unable to maneuver its head any where other than where I directed it. I never had to touch the snakes unless they were restrained.
I have no problem with tailing, I do it all the time. I do have a problem with free handling which is what you were doing in these picture. You were not using a hook or any restraining method and the snakes were too small to tail anyways. That is why I am concerned.