Not having loaded magazines in their rifles is what got a bunch of Marines killed in Beirut 22 years ago.
I stillhunt, usually with a flintlock, but sometimes with a percussion musket. The piece is capped and the hammer down. I generally hold the gun with the forearm across the crook of my arm and my right hand grasping the wrist. Moving slowly and carefully, which you should be anyway, there is no way that gun is going to fire until I raise it to my shoulder and pull that hammer back.
When I was in reenacting, I served as an ordnance safety inspector. One of the steps in the safety inspection was to see if the hammer would drop under pressure either from a steady push with the heel of the hand or a sharp blow with the heel. You would be surprised how many muskets were rejected even by a simple push. I know my guns have sound sears and tumblers, but I'll take my chance with the hammer down. Many percussion guns have a half cock position so low and main springs so weak that it wouldn't set a cap off at half cock. Also at half cock, you have another opening to catch a stray branch on in addition to the hammer spur. The force of it flying back can snap a sear in two, or if it goes back far enough, the fly in the tumbler will let the sear override the half cock notch which is what it is supposed to do.
So, I say whatever makes you feel safe, do it that way. Hammer down works for me. By the way, in the CW, troops normally did load only when in pretty close proximity to the enemy, mostly because of the chance that the powder could be dampened. Accidents did happen on the march, usually by carrying the musket muzzle forward over the shoulder (in route march, arms at will). In the cases I've read, the hammer was snagged by a low limb. When we loaded ahead of time, we didn't prime until near the enemy simply because of the fear that some of the men would be careless. And that is what it boils down to. If you're careful in handling your weapon, accidents won't happen.