Speaker wiring

I bought some inifnity Pr6500cs speakers for my 06 lancer and I'm having a little trouble wiring everything up properly. It's gonna be more work than it's worth to run wire to the door so I was wondering if I could put the crossover in the dash wired straight from the headunit speaker outputs and run new wire for the tweeters. Then wire the woofer output from the crossover to the factory speaker wiring. I assume you the factory wiring just goes straight to the speakers. Would this work? Is there a better alternative?