Here is the deal, depending on state law, those signs "No Concealed weapons" or "No loaded weapons" are usually not legally binding. They are not in my state either (Florida). You could legally carry, loaded or not if you have a CCP. However, know your laws.
HOWEVER, any store can have their own policy, forbidding you to carry, and if you refuse to abide by their policy, they can have you arrested or at least given a formal trespass warning. Remember, trespassing + having a gun (CCP or not) = an ARMED TRESPASS charge in some states (like mine) which is a felony and you lose your gun rights, ccp and possibly guns.
You are also under no legal requirement to disclose, but if asked to leave / unload, remove your concealed weapon, you MUST comply. Or you face arrest, or if you are lucky, just a tresspass warning.
You need to know your state laws.
I also do not see the logic in gun stores discouraging carry, but it's their store... you need to play by their rules. It could end badly.