don't know about compatibility between the SAT-Pro and the Wilkinson, but i can tell you the SAT-Pro has nothing wrong, it's a great trem and works flawlessly. if you ever get troubles with tuning stability, change the nut with a Graphtec or Tusq whatever those new selflubricating materials, be sure the string grooves are properly cut, wind the strings neatly around the pegs and stretch the strings until they don't lose tuning.
i do setups for local guitar players and on about a couple dozens SAT-Pro equipped guitars i worked on, i still have to find one that goes out of tuning even after Vai-ish abuse. no kidding
