Eliminating cats won't throw a check engine light on OBDI systems (I believe pre '96 computer systems) because there is no way for it to know. If you don't put the O2 sensors back in, you'd get the check engine light. On ODBII cars (I think 96 and later - what your other car probably was), there is an O2 before and after each cat, so it can detect a missing cat, so it would throw the check engine light.
I have a 90 and 91 both w/o cats and neither have a check engine light.