That is in essence not a bad approach, though it will also be sub-optimal (to some extent). The issue here being that when you only use a subsample to map your reads on you will never be sure perhaps some of the reads that align to your subsample would not have had a better (== true ) match against the rest of the genome/transcriptome. In theory you will have the same bias for all your samples so that might even it out a bit, but not eliminate it.

Bottom line: there is a risk to over-count the number of reads that map

Mapping to a truncated reference runs the risk of forcing reads to align where they do not belong. Don't do this. Align to a proper reference that contains all of the expected sequence.