I've dealed with the same type of analysis.

My solution was to do a pooled genotyping thanks to the GATK "best practices" pipeline, to obtain a single multi-sample VCF with the called genotypes of all my samples.

Then I filtered this VCF to obtain SNPs unique to each sample, for that you can use "SnpSift filter". (http://snpeff.sourceforge.net/SnpSift.html#filter), with the isVariant() and isRef() functions.

Merging is a good idea. You can do it like this:

1. bgzip all vcf files

$ parallel bgzip -c {} > {}.gz ::: *.vcf

2. tabix index these files

$ parallel tabix {} ::: *.vcf.gz

3. create a list of compressed vcf files

$ find -maxdepth 1 -iname "*.vcf.gz" > samples.txt

4. merge files, normalize and split multiallelic variants

$ bcftools merge -l samples.txt -Ou | bcftools norm -f ref.fa -m - -o merged.vcf

5. filter merge vcf file for sites, where only one sample has at least one ALT allele and create a new vcf file for each sample with its private variants

$ parallel "bcftools view -i 'COUNT(GT=\"alt\") = 1' merged.vcf | bcftools view -x -s {} -o {}.privat.vcf" ::: `bcftools query -l merged.vcf`