What employable manual/physical skill will never become obsolete?The only manual skills that will never become obsolete are performing arts and human to human contact.
Performing arts like dance cannot be replace, because there is a pleasure that comes from watching other humans excel in motion. Even the most perfect eye-deceiving robot will not satisfy that need.
Human to human contact can't also be replaced. whether we are talking about a massage or prostitution, the idea of being a human makes everything feel different.
I am pretty sure that we will have all sort of technologies that try to deceive us from the human experiment, but the more we replace human interactions for machine interactions, the bigger our need for human touch will be.
(disclaimer: I am not supporting any argument in favor of prostitution.)