Blasting reads sounds like a bad idea considering small lengths and the number of reads. May be you can shuffle few thousand reads (seqkit?) and then try it, however, I will suggest using fastq-screen to map reads on the genomes of organims that you suspect to be present in your raw data.

You need taxonomic profiling softwares, like Kraken and Kaiju . BLAST is the slowest for this kind of task.