Istvan, thank you very much for introducing me to an alternative way of thinking about this.
While this is useful, my situation calls for an ability to detect all variants, both known and novel, in a selected region as opposed to known variants only. Also, all of my sequence files are BAM -- i.e. they are already aligned to a reference genome. While I could still use the k-mer based approach you mentioned for BAM files, I'm just curious if we could extract per-base reference allele information directly from BAM files, since this information was used to align the reads in the first place.
Ultimately, I was thinking about a variant calling pipeline for aligned BAM files where I use a tool like samtools mpileup to get pileup data and then parse it to call variants. Again, I'm aware there are other famous callers such as GATK's HaplotypeCaller and bcftools -- this new pipeline I'm thinking about is specifically for generating an input VCF for my other Python program (I can get pipelup data with pysam.pileup).
I was thinking I wouldn't need a reference genome if we can distinguish REF vs. ALT alleles in the pileup or in the BAM -- does anyone know if this is possible (e.g. using certain BAM tags)?