When I obtained my first hammergun I received this great advice from our own Uncle Bob. Great stuff.
Steve, I cock my gun as I mount the piece, cocking one hammer as a part of the mount, as I would slide the safety off during the mount, with a hammerless gun. If I need the second barrel, I lower the gun a bit and remount as I pick up the second bird, and again cocking the hammer, this time the second one.
I have found that there are a number of reasons why I prefer to not cock the hammers and hunt with the gun open.
First is the fact that an angular gun (as opposed to the straight line of the closed gun) hangs up on cover. No concern if one is riding up to a brace of pointing dogs in a mule drawn wagon, but a very real one when one is walking them up.
Secondly, when the gun hangs on cover, you will dump the shells out of the breech more times than not. Now you are hunting for shells in the cover, mud, or snow, instead of birds.
Third, and maybe the most important, cocking a hammer as part of the gun mount is not more than a very slight fraction of a second slower than sliding the safety off and is a compatible part of the gun mount, as the gun mount is used to acquire lead on the bird. To postpone the mount when a bird flushes while closing the gun disrupts the timing of the mount and leads to misses. I thing that is why Lord Ripon and other great wing shooters of the 19th century received their guns from the loader closed.
I realize that there are times when you hunt a pointing dog that you will have time to close the gun and walk in with the hammers cocked, but that is not true every time, when hunting a pointer on prairie birds. Two different mannerisms will sooner or later lead to needless misses.
Fourth, lowering the gun to catch the second hammer will make one a better shot on the second bird, than it would be with a hammerless gun because it reestablishes the movement of feet and lead hand in establishing the swing and lead.
Well, there you have it. Why I hunt with the gun closed and the hammers un-cocked.
I do think with very little practice cocking the first hammer as you mount the gun, you will find that it is very easy to do and quite natural. You will also find that a hammer gun is not a handicap to harvesting the three of four birds a day that we are allowed. It will indeed provide you with a new and enjoyable element