Actually, that's not quite right. The suspension of rights is a distinct act on Congress' part... it doesn't automatically attach to any warfighting. The "president's power to wage war" is entirely constrained by Congress' Constitutional powers. It's just that they delegated many of those decisions to the executive in recent years (war powers act, etc).
It depends upon which ones we are referring to. Some laws provisions are engaged upon a declaration of war. Then there's that whole habeus corpus thing that the President may do.