You could build a reference database that contains sequences of the particular cyanobacteria, algae, and chloroplast species you are interested in. The use classify-consensus-vsearch to find the closest matches.
But it sounds like your classifier may have already made that distinction: true cyanobacteria are probably not lumped into class chloroplast in your reference database, but you will need to check the taxonomy to be sure. I am not familiar enough with cyanobacterial taxonomy, though, to say whether these are likely to be confused with chloroplast DNA.
You make a good point — if cyanobacteria are an important component of the microbial communities that you study, then it is probably not wise to throw all of these out unless if you can differentiate cyanobacteria from chloroplast (which, again, I think the classifier/taxonomy already does).