SNP-phenotype association analysis only using the SNPs on a specific gene
I know that the GWAS association p-value threshold is 1e-8


This may be a common threshold of statistical significance that is used, but it's definitely not an absolute value. It's a hack to try to work around many issues with GWAS associated with testing millions of SNPs. Unfortunately, the most relevant issue in GWAS (for spurious significance) is unexpected shared genetic structure in the cases or controls, and this cannot be excluded by a p-value threshold, regardless of how low it is set.

In your 100-SNP example, you are correct that the bonferroni correction would be a threshold of 1e-4 (for a desired significance threshold of 0.01), but it's important to be cautious about GWAS results, even when the p-value indicates otherwise. Trust no one, especially yourself. P-values should never be used as an indication of importance (which suggests that most GWAS results should probably be reconsidered), and are better used in conjunction with other evidence for identifying relevant / significant tests.

My recommendation for GWAS (or any similar bulk genotyping study, as in your 100-SNP subset) is that at least a bootstrap sub-sampling process is carried out, to make sure that observations found within the comparison of interest are at least well replicated when comparing smaller sub-groups of the cases and controls. More information on that can be found in the poster I presented at Queenstown Research Week last year, and detail about the implementation in my draft preprint (which will probably never be properly published, given how old the research is).