"knowingly" is a legal term of art. It stands by itself in that sentence. It distinguishes the law from a strict liability statute. it means only that the actor was aware of his acts.
It won't be read as you have suggested because to do so:
1. It would have to be read to require that the actor not only knew of the sign, but the law as well, and knowledge of the law is not an element of a crime; and
2. It would render the word "conspicuous" meaningless, because people who didn't see the sign would not "know" even if it was conspicuous, and people who did it see it, even if it was not conspicuous, would "know." The courts are loath to read such specific language out of the statute with a strained interpretation of "knowingly"
Thank you for your detailed answer. I will error the side of caution and if I'm ever in Ohio I will watch for and honer no gun signs.