I don't think there is any reason you can't sink-wash cycling shorts with dish/hand soap. Just make sure you rinse them out well and the soap leaves no residue. Don't wring them out, you can blot with a towel and hang dry.

I am prone to skin infections and never wear cycling shorts more than one day. Salty sweat abrades both fabric and skin so the shorts and nkfrench will be in good repair longer with clean shorts. I machine-wash them in cold water with my other clothes. Tide coldwater detergent, no scent/softeners. I have been told not to machine-dry them, they do go in my clothes drier on low setting just for convenience.

The investment in enough bike shorts to make it through 2 weekends and the workweek was well worth it to me. I don't like adding chores to do when I get home from a bikeride.