Use one of the tiny dogs as bait to lure the snake. Leash it in the center of a wide open room that you can close off quickly. When the snake come for the dog, nab the snake.
It's similar to what a member of the U.S. Army Corps of Engineers once told a relocated 'Yankee' that lived close to me. His, the relocated Yankee, dock was next to mine and one morning I went down to the cove and he's standing there looking into his boat from the shore and he seemed all upset. I asked what was up and he said he came down to go for a boat ride and saw a snake go from the dock into his boat and then under the floor/in the bilge. He was horrified of snakes and wouldn't go near the boat. The lake is man made and the U.S. Army Corps of Engineers oversees it and for some reason he called their regional offices to see what to do about the snake in his boat.
He told the Corps guy what was up and the Corps guy asked him; "do you have a small dog?" My neighbor said that he did. The Corps guy said; "put the dog in the boat, when the snake goes to bite the dog, shoot the snake," and then he hung up on the relocated 'Yankee.'
I laughed, told my neighbor to wait a few minutes, went to my house, threw some rags in a bucket and poured ammonia on them, filled a spray bottle with ammonia and headed back to the cove. I tossed the rags in the bilge, sprayed in more ammonia through a few access openings in the floor, and before long the snake was in the cove rather than in the boat.
Entertaining critters, snakes are. At least the wild ones around here are.