IIRC, "My Father's Shoes" was a fretted bass, but about as thumpy as Mark King has ever gotten!
He did use a fretless on that album, on the track "Seven Years". It was a Moon jazz bass that he got for free at an airport in Japan, which he defretted himself. There is some confusion about this, some people think he used it on the track "Lasso the Moon", although that was recorded with a Wal bass with a midi pickup.
As for Mark using the Stingray to record most of his stuff, this is completely untrue. Mark did not get his first Stingray until 1991 (it was a 1991 serial number). He did use a Stingray and a Stingray 5 string to record some of Guranteed, but then he also used a Status Matrix Empathy, a Wal and a Moon jazz bass on that record too! The only record that was recorded completely on a Stingray was "Forever Now" in 1994. Perhaps the Stingray explains why the bass tone on that record is so utterly average, especially given Mark's former glories?
Likesay, before Guranteed, his last recording bass was an Alembic on "Staring at the Sun". And before that it was mainly Status, Jaydee and Pangborn he used.
At the end of the 1990's he seemed to be having a bit of a jazz bass thing. He used the Fender Mark King jazz and then used a couple of GB basses (though these didn't sound very good either, they never had enough tonal defition imo!) before going back to Rob at Status and coming up with the Kingbass design.