Pathway-specific polygenic risk scores (pathway-PRS) measure aggregate genetic risk across single nucleotide variants (SNVs) annotated to genes in a pathway of interest. In most applications, SNV-to-gene annotation is based on SNV position with respect to gene boundaries. This approach is ill-suited for incorporating non-coding SNVs, which can regulate gene expression over long distances and represent a large proportion of risk variants for Alzheimer's disease (AD). Here, we compare the performance of AD pathway-PRS across SNV-to-gene annotation strategies that integrate varying levels of functional genomic data, including adult brain chromatin interaction and expression quantitative trait loci (eQTL) data. In the UK Biobank (n=328,526), including AD cases defined by ICD-9/10 codes (n=3,043) and by family history of AD/dementia (n=38,589), we show that the annotation strategy integrating chromatin interaction and eQTL data consistently improves pathway-PRS performance. We replicate this finding in independent data from the Alzheimer's Disease Genetics Consortium (n=3,370). We further find that pathway-PRS associations with AD vary by annotation strategy and that power to detect sex-dependent and age-at-onset associations is increased with integrative annotation. Together, these findings support the use of functionally informed SNV-to-gene annotation for pathway-PRS construction and highlight the importance of applying multiple annotation strategies for robust inference.