I believe the wiring harness, relay and switch are the same for the Cobra fogs as they are for the GT/Mach 1 fogs. The pigtails are slightly different as the bulbs are different than the regular fog light bulbs.
I would recommend picking up the proper pigtails from Latemodel Restoration or somewhere..they aren't very expensive and will save time/headaches down the road.
Below is a link to VMP's page with a full fog light install write up. The wiring portion should be identical for both Cobra fogs and regular fogs.
01-04 V6 CLEAR GT Foglight Kit: VMP Tuning - Superchargers, Tuners, Custom Tunes, & Performance Parts
Keep in mind also that the cobra bumper will fit much closer to the stock v6 bumper. You may have to relocate the bumper top posts back ~.5" or so to re-clip the bumper for better fitment between the hood and bumper.
12 Black GT500 SVT PP l 2.6 Pulley/Idler l Airaid l o/r X l 305 NT555R's l Recaros l
04 Azure Blue Mach 1 / 03 Sonic Blue 3.8 / 14 Sterling Grey F150 FX4 402A 5.0 / 11 GT500 R.I.P.