It turns out dinos will also pass through a coffee filter although the coffee filter does get clogged pretty fast. It might be best to pass through a course filter first to get rid of most of the detritus then pass the rough filtered water through the coffee filter. This might be a better method since I doubt any significant amount of cyanobacteria will be able pass through a coffee filter.
Here's the shaken siphoned water
Freshly filtered water
After about 8 hours
It did seem to take longer for the dinos to gather back together after passing through the coffee filter. I'm not sure if this is because less water was used (since the filter became clogged) or because less dinos were able to pass through that filter size.