Did Cádiz civilians know they were trading with blockaders?

Did local civilians realize they were trading with the ships blockading their port?

Yes; they knew about the blockade and sustained a limited small-boat trade while the British kept more dangerous shore contact at arm's length.

The civilians understood both the war and the blockade. Small boats moved between shore and squadron, while the British sometimes resold permitted goods taken from intercepted vessels. Trust had clear limits, because blockaders did not casually visit local taverns or surrender control of the exchange ashore. The same boat traffic nevertheless supported regular washing of bedding and clothing. That cleanliness helped the Royal Navy preserve crew health in the Mediterranean heat.