Not having "show" cochins, I have never experienced any issues with fertility with my cochins. Guess their butts just are not fluffy enough to prevent that cloaca kiss as it is called. I still think that my boys and girls have enormously fluffy butts, but guess not as fluffy as the real "show" birds, smiling. Maybe I don't want real show birds, cause I really don't like to pull feathers from butts.
I have watched my flock of cochins mate and I certainly can see that kiss occur, it is surprising how much of the vent protrudes when contact is made, very interesting. I remember one time touching a vent of one of the birds to get off some little hunks o' poo and I was surprised to see what the cloaca did. The vent looked like it was a mouth chewing gum, only way to describe it, guess that is the action that draws the sperm from the male within the body of the female. Kind of gross, but it was kind of funny at the same time. It is good to know what action our birds do, smiling.
Sebas is right about the feathers. I once heard a fellow telling me that he was going to cut the feathers short on the female, in hopes of great fertilization because of the fluffy butts of his wyandottes. Oops. I told him to not do that, you pull them out, if you cut them, it makes the feathers sharp and after a try the rooster will certainly not mate. He has a very tender cloaca too....
When you remove the feathers, also, listen to what Sebas has said, about where to pull the feathers out. When I went back to see this fellow that I had been speaking to about pulling out the feathers, I was kind of shocked at what I saw. He had pulled most of the feathers off the rear of the chicken, she (they) looked pretty bad. Guess he thought it was the entire area that needed to be void of feathers. Very wrong, very wrong. Focus on the feathers, as you were told, the ones above the vent with the females, below the vent with the males. It may make a huge difference in the touching of the parts to allow better acceptance of the sperm. Good luck, would love to hear if you notice a difference.
Remember....DON'T CUT THE FEATHERS, PULL THEM GENTLY OUT.
When I clean the back ends of my cochins, and I do that regularly, to remove poo balls, I sometimes will have to pull out a feather or two, because they just seem like there would be no point in trying to clean them off. I don't even think that the birds notice that feather pull. Thank goodness it is only now and then that there is a necessity to pull out an entire feather, but that is my experience, it doesn't bug them much at all. Don't pull out too many feathers, they still need warmth for their fluffy butts to be warm and cozy. Have a wonderful day, CynthiaM.