Do LDRs have higher distortion than other volume controls?

Technically yes, but well below what's audible. Distortion specs are often used as a rough proxy for sound quality, but humans can't reliably distinguish distortion below roughly 1% in normal music -- so a component rated at 0.001% THD won't sound different from one at 1% THD. If distortion specs alone determined sound quality, everyone would just buy whatever measured lowest; nobody actually shops that way because it isn't meaninful to actual human experience with audio equipment.