"Does(did ?) the stickshaker in the 757 have any connection to the static port?"
Not directly. The static ports are attached to the Air Data Computers... and the Air Data Computers feed the Stall Warning Computers... and the Stall Warning Cards operate the stickshaker.
Amongst many other things, the Stall Warning Computers need CAS, TAS and mach. These are provided by the Air Data Computers. Pitot-Static sensing elements are needed for the Air Data Computers to compute these.
Regards.
Q.