The only computer FX they had then were mostly animated elements - phasers, shields, transporters, generally anything "electrical energy based" - and maybe an LCARS display here and there. There were a couple of holographic map/planet elements used in "The Last Outpost" and "Contagion", but I don't remember too much beyond that. Those would be the only other things that might have to be re-done with modern CG.

Remember, we're talking about 1986 to 1994 here. The Genesis planet animation in Trek II and "The Last Starfighter" were state of the art only a couple of years before, and "T2" and "Jurassic Park" only showed up in 1991 to 1992 and at the time were way beyond a TV show budget and schedule. In general, Trek TV didn't start to use CG on a regular basis until about halfway thru Voyager, around '98 or '99.