I haven't had a snake issue with my chickens, but I have battled diamond backed water snakes in my pond. When the snake ate the only fish with a name, it became war. Snakes are extremely difficult to catch in water, I started taking my housecats into the pond area with me, and eventually one of them cornered the snake under a chair. He met the shovel. I then put dusting sulfur all around my fence line, they don't like it, tends to make them irritable and more likely to bite, but usually they won't cross it.
I like the twisted bird-mesh idea. And if I were investigating a coop that could have a snake hiding in it, I'd have leather gloves on, and a cat or dog with me to spot things I might miss. and some kind of tool for head removal. I find rose snips come in quite handy.