Sorry I'm late getting on to this thread, but thought I'd add a note about my experiences. I have a 1/4 acre spring-fed trout pond in western Virginia. I've been battling Chara since I bought my place in 2002. Normally, my pond too is crystal clear (except after unusual storm events); and the water from my spring is very, very mineralized -- these conditions, I've found out, are just prime for potentially huge Chara infestations. I gave up on mechanical removal two weeks into my first summer -- Chara weighs a ton!
I now regularly use Cutrine Plus granular and a fairly low dosage of Aquashade. I don't think these have had any ill effects on my trout. From what I've been able to research, if your trout originate in a hard-water source hatchery, the effect of copper treatments (done according to directions) is minimal. If the trout came from a soft-water source hatchery, then you should probably avoid copper products. My trout came from a local hatchery with spring water as hard as mine -- hence, I've seen no ill effects.
By the way, I also have an aeration system. And, in agreement with an earlier post, it seems to have no negative effect on Chara.