You can actually, in the camera flash control menu, turn off the flash firing although the focus assist will still work.
Really? I've literally never seen that - or is it a new 5d3 feature I've just not spotted yet? And I thought I'd been through every setting 
No, I've seen it on my 5d2 as well. It's in the External Flash control menu. I think. Maybe it's elsewhere, but I've used it in the past.
Thanks! I'll take a look..