I'm sure there are businesses that may rather see OC over CC, so post accordingly. Without a door-to-door survey; however, this is pure conjecture. I've read this sentiment in the public, so it's not unreasonable to apply it to private businesses.
That said, unless you know the owner and his/her/their stance on OC when showing 30.06 signage, it could backfire. Hopefully, they'll give you verbal notice and give you a chance to correct it before bringing Johnny Law in.