I would say no walking would be the ideal choice, but I can't say that it would screw up the hunting on the place, unless that's all that's going on.
I have game camera photos of me on an ATV and deer coming by 20 minutes later, so at least in our neck of the woods walking through might cause a minor, immediate disturbance, but I don't think it would result in any significant change an hour or so after the fact. But that's just where I hunt, I can't say for anywhere else.
Because my property is so small, I have declared almost the entire place a "no go zone". I only hunt the edges of it and only with the wind in my favor. The only exceptions are for the recovery of deer and mid/late winter woodcutting.
The biggest problem this creates for me is that my wife likes to come down and hike. She argues that it is just as much her property as it is mine and if she wants to take a walk in the woods, she can. Of course she is absolutely right, but I still manage to get twitchy when she does it. I'm a jerk, I know.
Thank God I have a nice stand of hickory right next to the cabin that allows me to take the kids squirrel hunting w/o disrupting much. I could not live with myself if I gave my little girl static about wanting to squirrel hunt during deer season.