"Converting" the data to sam/bam requires alignment.
No it doesn't! Using the BBMap package:
reformat.sh in=file.fastq out=file.sam
Completely valid sam file, really fast! :) Also that will ensure the final VCF file is extremely small and easy to work with.
*Disclaimer: I do not recommend this approach.
You should figure out exactly what you are trying to do and understand the whole process before trying to find "the fastest tools".