There is a product on the market called Scotch Barley bales.
Supposedly when barley straw decomposes it releases a chemical which
is an algaecide. It is used in fish ponds so I doubt it is very
dangerous to mamals. I have never used it. You might try collecting
your own barley straw and putting it in a nylon mesh bag so it doesn't
get all over the place. The articles I've read state that wheat straw
does the same thing but it is less effective. The commercial product
is quite expensive compared to what the highway departments pay for it
to use as a mulch on newly reseeded areas of recent road construction.
Do a Google on Scotch barley bales for information from the folks who
sell the stuff commercially.