Yes you can! First, you must remove the air bladder from the exterior shell per your products owners manual.
To hand wash, take a rag or a brush with some hot, soapy water and scrub the area you want to clean. If you are seeking a deeper clean, you may put the entire exterior nylon shell in a conventional washer and wash with mild detergent on the delicate cycle (make sure all buckles and Velcro strips are secure). Let the product air dry once you are done cleaning; DO NOT PUT THE NYLON SHELL IN THE DRYER.