Cochins have soft feathers, not hard feathers like most chickens. Therefore they become easily matted and dirty, especially the vent area and feet.
It's very easy to give them needed "tune-ups."
Fill a small rubber wash basin with warm water with half a cap-full of children's liquid bubble bath. I use the sensitive skin/no tears formula.
Back your Cochin up to the edge of the tub, keeping the chicken's head under your arm. With your free hand, splash warm sudsy water onto the crusty rump until the crud softens, then take a tooth brush or wash cloth and gently stroke the feathers in a downward motion, careful not to irritate the skin, until all soil is removed.
For the feet, retain the same position, lifting one foot at a time into the tub. Use your fingers to loosen the soil, then use the brush in the same one-direction motion to remove all foreign particles. Pay attention to fecal matter accumulated in dimples on the bottom of the feet.
No rinsing necessary. Blot excess moisture with a towel and air dry on nice days, or use a blow dryer.
My chickens all get tune-ups regularly. No need to wash the entire chicken, though, just the offending parts as outlined above!