Although I am not quite clear what you mean by the alarm giving you issues, I don't think you will have any issues. The OEM radio came in the car from factory so if you have an aftermarket alarm system, it should work with the stock radio. I have never seen someone have to change their stereo in order to install an alarm system.
If you are talking about some security that the OEM radio has, it would probably just need a code, which the owner should have or you can just call the dealer. I have never seen a stock Integra stereo in person so I don't know how hi-tech they are, but I know that's the case for newer ones.