Yup, hook up a relay. Get a 12v relay at radio shack, SPST, like so:
As you can see from that diagram, you have four poles, 85, 86, 87, and 30.
If I remember correctly, 30 is power for the fans, going into the relay, 87 is power for the fans going from the relay to the fans. You need to apply voltage (12v, any small amount of ampage would work), across 85 and 86. So ground 85, and put a 12v source to 86, with your switch in the middle of it. I'm using the yellow (15a I think) fuse below the one you pictured, since I believe it was for a system that was no longer in use, but still powered. I wired it like yours, with an inline rubber insulated fuse holder (also at Radio Shack) with a 15a fuse in it.
Disclaimer: I'm no electrical engineer, so I make no claim that this is the best or correct way to do this, or that I've made no mistakes typing this. I do however have four of these exact relays in use in my car, that have been working for years, including exactly this situation, using one to power my fans with an on/off switch.
Edit: If you're confused, you can't see it in the picture, but on the bottom of the relay, in very very small print, are numbers labeling the four poles.