I don't shop Wal-Marx personally, so I haven't had any direct experience with this. I did have a weird experience recently where I drove some dope fiend to a methadone clinic while I was carrying. They had a guard (himself unarmed)there, but no posting about carry that I noticed. Whereas it may have been legal for me to be there armed, I didn't have any business inside, and I didn't want to instigate what would certainly have been a bad scene, so I stayed in the car. Drug addicts are prohibited persons, but a chauffeur for one should be OK, right? Pretty fine hairsplitting to the cops though, so I didn't press the issue.
My understanding is that Wal-Marx's official policy is to follow state law, so absent any posting, you should be legally OK. Tell them to throw up a sign if they don't like it, and then tell them you won't do business there if and when they do.