Simply put, no.
The problem you have is that what you refer to as the "sub" is nactually the whole brains of the "speaker system". Along with the subwoofer and it's amp, that box also contains all the amplifiers for all the other speakers in "the system", and possibly a 5.1 decoder as well.
So, as you can see, there is a whole lot more involved than just replacing the subwoofer (which is the brains of the whole system) with a "regular" subwoofer. At this point, you might want to start looking at receivers and separate speakers.