If you use a non-nitrox computer while diving nitrox, two things happen: (1) you don't get the benefit of extended bottom time that you can get with nitrox; and (2) you don't track your O2 exposure, which is an issue for oxygen toxicity, primarily pulmonary oxygen toxicity. Lots of people (I am one of them) often dive nitrox with the computer set to air, or with air tables. This means that you get an extra margin of safety, because your actual nitrogen load is less than the tables or your computer is assuming (taking into account the theoretical nature of the nitrogen loading assumptions). So you can use your non-nitrox computer to dive nitrox. You will just be trading one benefit of nitrox (extended bottom time) for another benefit of nitrox (extra margin of safety). But what about the O2 exposure? As long as you are diving a typical recreational dive schedule of two or maybe three dives a day, you are not going to have an issue. You have to do some pretty intense diving to get into an O2 clock issue.
So go ahead and use your regular computer, just watch the MOD (as others have noted - CNS O2 toxicity is nothing to take lightly) and don't try to wing it on extending your bottom times. If you are doing multi-level diving, I would guess (and it is only a guess) that you will not benefit (in terms of bottom time) from using nitrox tables over an air computer, because the tables still assume a square profile. It is not necessary to put your computer in gauge mode or ignore any bottom time remaining calculation.