Check with Autometer regarding the specific part number you're looking to purchase? Intuitively a mechanical speedometer wouldn't use a VSS, that's if you buy an electric / electronic speedo which Autometer also makes. Mechanical speedometer implies a gear run off the tailshaft turns a cable which is connected to the back of the speedo. If you instead wanted an Autometer electronic speedo, you could use your existing VSS.
It is possible that without a VSS (you'll have to remove it to install the cable if you get a mechanical speedo), your computer will no longer know how fast you're going, so it may impact some part of the tune and your car may experience driveability issues as some functions are driven by vehicle speed. I wouldn't recommend it, unless you disconnect your existing VSS (and run with no speedo for a while) and verify that everything still behaves as it should, or unless you've converted to a carb.
If you use a mechanical gauge, numerous posts online suggest you'll want a C4 automatic transmission cable. The C4 was used commonly in much older Mustangs (first gen, and II), so you'll just want to make sure the cable length is adequate and search for a 1964-73 automatic speedometer cable.
Personally don't know why you'd want to install a mechanical speedometer. Noisy, requires gear changes to calibrate to tire or rear-end changes, etc. 1960's tech at best in a car that already supports a modern, reliable, accurate, calibrateable electronic equivalent.