There has got to be some kind of dash kit for that car. Wouldn't this work?
Amazon.com: Stereo Install Dash Kit Honda Accord 03 04 2003 2004
Power wire is super important. No 4 gauge is not only for 1200watts and above. The bigger the gauge cable, the lower impedance from power source to amp. Just because you have very low impedance and more power than is necessary at your disposal doesn't mean that it will hurt anything. Beside, you will probably want to upgrade your equipment soon enough. We all do.
Again, do it right. Don't cut corners, it will cost more in the long run and take way more time.
You gotta figure out a way to replace your stock HU.