I've run an Eagle with 114% power demand successfully before now - just use the priorities to switch off things you don't need. As mentioned, the weapons only draw power when deployed, and you can't use the FSD with them deployed anyway. The way I do it is:
Priority 1: thrusters, shields, life support, sensors - basic stuff you need to be always on in order fly (safely)
Priority 2: weaponry, ECM, maybe kill warrant scanner, etc - stuff that gets 'deployed' and that you need to be active during a fight
Priority 3: FSD, fuel scoop, interdictor - maybe the KWS goes here if it's really high power - stuff that you need when you're not fighting, that you don't mind getting turned off when group 2 is active
Priority 4: cargo hatch - stuff you really don't care about
If you KWS is really high draw you might have to manually bump up it's priority when you need to use it, otherwise there's no good way to keep it powered up that doesn't sacrifice something essential
I also turned off the voice warning for 'modules disabled' because that gets old fast
The Eagle is fun - and part of that fun is managing the power demands.