Weddings: Anything imprudent about a small, fast prime-exclusive kit?

Greetings all,

I've got a raft of weddings to attend in the spring, and I've been asked to serve as a second photographer at two.  I've done engagement photos for both couples with my personal Fuji gear, but I've decided to rent a Canon body (likely the 6D) for the weddings. The question is whether, in your experience, weddings present unique obstacles to the exclusive use of a small set of fast, non-stabilized primes.

In addition to the 6D, shoe-mounted flash, and diffuser, I'm considering the Sigma 35 1.4 and Canon 85 1.2L II.  These primes represent the sort of shooting experience to which I've grown accustomed and with which I'm very pleased. Given my lack of professional wedding experience, however, I'm concerned that I might be at some kind of disadvantage without more versatile optics (e.g. a stabilized standard or tele zoom).

I'll be carrying my Fuji gear as an insurance policy, but if I'd be at a disadvantage with the Canon primes alone, my Fuji gear is not going to solve the problem.

I'd be very much interested in, and appreciative of, the perspectives of anyone familiar with the rigors of wedding photography.

Regards