Except the 70-300L I've just mentioned I also have 24-105L and Sigma's 50mm.
Well, you'd be woefully under-equipped for any indoor wedding. So, unless you are waiting until next summer, chances are any wedding for the next 6-8 months will be indoors in some fashion. There you'd find that the f/4 of your 24-105 and the variable f/4+ of the 70-300 would be very lacking, forcing you to shoot really high ISO, or 1/30th second shutter speeds. It's gonna result in a lot of blurry photos.
A flash is gonna be critical, as it'd help you get away with f/4 lenses somewhat, but I'd suggest finding a low light prime or two. The 35L would cover that, along with your 50mm from Sigma. If you swapped the 70-300 for the 70-200 f/2.8 you'd have a pretty classic wedding shooter's kit. The other option would be to grab a longer prime (85/100/135) and just keep the 70-300 for outdoor stuff.
Flash will help you get away with most things, except for an indoor church ceremony where they won't allow flash. Only low-light primes will save you there.