They let Ken Norton and Thomas Everett go after the 92 season and the cap didn't start until 94.
If Jimmy had stayed he likely would have continued to replace veteran with draft picks with or without the cap.
Haley and Novacek were cut or retired because of injury issues (back surgery for Haley and back issues for Novacek as well).
The 94 season NFC championship was doomed by the Erik Williams car wreck injury.
Jerry cut WR Jimmy Smith in 94 because Smith won an appeal when Jerry tried to pay him 100K instead of the 350K he was due from being on the Non-Football Injury list in 93 due to appendicitis.
If Jimmy had stayed and Jerry had let him run the football operations like Jimmy had done for 5 years, then the cap wouldn't have been a big problem for the Cowboys.