Copyright in regards to sound effects is so tricky. You're likely to hear a lot of the same things over and over again once you start listening for it because of that. Hollywood likes to completely ignore copyright law in sound effects, for example, and they're so hard to prove ownership of that it's usually not worth the court case. And then we, as an audience, get used to hearing that sound in association with certain things and it becomes what we believe it sounds like, regardless of reality. I mean, how often have we heard a sword go "shing!" when it's pulled out of a scabbard? In reality it sounds a lot more like "shunk". If you put that sound in a game it will sound wrong and dull. So, yeah, if that's the sound that you associate with an incoming bomb, use it to your advantage.
I think modifying the default sounds is a great idea, there's also a bunch of sound effects over at open game art, maybe you could find something appropriately alarming and then mix it up to make it more you.
I always like it when games have their own sound identity. When you hear a blip or woosh and are taken right back to that game.