But about a third are extraverts. As for being more fearful or timid, it's just that we pause to check things out a little longer, which can look to others like fear. Different purposes require different strategies. Then there are the reactions you may get. A person you want to treat you differently may be delighted to oblige, once you explain what you require.
Examples are service persons, health professionals, and friends.
But a few are bound to see it as an excuse for wanting special treatment. I know I can sometimes sense when I'm going to get that reaction. In those cases I may choose a different approach, or not speak at all. Tell them it has both meanings, but you mean sensitive to sensory stimuli. Reassure them that they are empathic, if they are, and that HSPs when overaroused may not be very empathic at all.