Lystamta amboinensis(skunk cleaner shrimp) do not eradicate or control crytocaryon irritans. They feed on damaged skin and some external parsites. While they might pick up an ich parsite or two' there is no evidence to suggest they are on their menu. Even if they did pick a few off while picking at the damaged skin, they wouldn't touch any of the encysted parasites or those in the fish.
While we are on the subject,another popular biological cleaner is the cleaner wrasse; same story ,unfortunately:
Alexandra Grutter The stomach contents of Labroides dimidiatus(cleaner wrasse) were examined by Alexandra Grutter Their diet consists of gnathiid isopods, scales, copepods and non-parasitic copepods (Grutter, 2000). No crytocaryon irritans was found.
As for the notion that using a cleaner shrimp is safer than proven treatment methods, it is clearly more dangerous to leave cryptocaryon irriatns in the tank without an effective treatment.