In my opinion, in this case, the selection of alignments should be done by filtering existing alignments and not by "forcing" the aligner to behave a certain way. Look into the SAM format specification and note how imperfect alignments are annotated.

For example, the NM tag will contain the value of the so-called edit distance to the reference. When that value is zero the query matches perfectly.

If, as in your definition, every alignment with a change should be called unaligned then filter for the NM tag value that is larger than 0 and select your aligments that way. If retaining a BAM file is essential you can even flip the flag to be unmapped.

Check out the penalty parameters --mp, --rdg and --rfg which you can set to something like 10000, the number of allowed seed mismatches -N which you can set to 0 and the option --very-sensitive to enforce stringent end-to-end alignment (the latter actually already contains seed mismatch of 0). Together these should discard every non-perfect alignment. Additionally you could be stringent with the post-filtering towards MAPQ to only keep very unique reads, e.g. with samtools view -q 30.