I have hyperacusis, mostly with high tones and s-like tones. Can these tones actually damage my ears (even at low volumes)?

Depends. Finding the reason for your decreased sound tolerance is important to determine if excess exposure to sounds will lead to damage. Usually there is no risk for damage from normal levels of sound exposure even if the sounds are perceived as loud. A thorough audiological evaluation will determine the nature and possibly the cause of your sound sensitivity. From there your question can be answered.