Perhaps a quarternary ammonium compound (like Physan) would work better - that is more likely to disrupt the algae cells, while having less effect on the orchid leaves' cuticle.
The Physan bottle claims that it is non-phytotoxic, which seems counter to claims of being an algicide, however.
From a google search for physan:
"Physan20 is a broad range disinfectant, fungicide, virucide, and algaecide which effectively controls a wide variety of pathogens on hard surfaces and plants"
Of course, I've seen marble being called organic, so go figure...