Carrying a wand as part of one's birth right had nothing to do with blood status. It was a simple observation that Rodolphus made about owning up to who you are regardless of where you found yourself or who else was around. That was one of the main problems he'd seen with Muggleborns and Half-bloods. They were willing to give themselves up so they could be accepted by the majority of the world rather than embracing what made them different.
"What brings you out to the dock today?" he continued with what ought to be a pleasant enough conversational piece to appease the majority of individuals around here.