I'm not entirely sure what the issue is: is it hum in the file? A problem with the playback, amp, connection, etc, or is it for sure just a physical resonant frequency?
I've actually never (yet!) built an arcade cab but I'm a musician/producer/etc. by trade. (Far from an expert on the physics of it, tbh) but if it's merely a matter of resonance there's probably a few ways to mess with it: adding some mass to the walls of the cab would change the resonant frequency and possibly alleviate the problem... but having a different resonant frequency MAY cause an issue with different sounds/tunes instead. Ports (basically, holes in the thing) would have an effect on the resonance as well. Even stuffing part of a blanket or tshirt into the open areas can completely change the frequency response on the system. Even changing how the speakers are mounted could do the trick.
DietCoke is right though: if you're only running into a problem on one game or specifically one sound, probably the best solution would be to simply edit the offending sound and call it good. If it's just one file and you can provide it to me and describe the issue in more detail I can take a look and see if I can fix it. Since you're saying 'hum' I'm wondering if it's actually a problem in the file instead of the build.