I've been hunting with hammerguns all my life. [Well since I was about 7] and have never had much trouble cocking both hammers at a flush; [either grouse or woodcock] in enough less time than I could push a regular "safety" to make a difference. It is a bit more tiring to carry a hammergun at the ready, and a bit slower to get hammers back from a low carry position, but not enough to matter. If you are not "ready" you can't get a good shot off with any gun in close cover.

All the best, Mal