The field of conservation genomics is becoming increasingly interested in whether, and how, structural variant (SV) genotype information can be leveraged in the management of threatened species. The functional consequences of SVs are more complex than for single nucleotide polymorphisms (SNPs), as SVs typically impact a larger proportion of the genome due to their size and thus may be more likely to contribute to load. While the impacts of SV‐specific genetic load may be less consequential for large populations, the interplay between weakened selection and stochastic processes means that smaller populations, such as those of the threatened Aotearoa hihi/New Zealand stitchbird (Notiomystis cincta), may harbour a high SV load. Hihi were once confined to a single remnant population, but have been reestablished into six sanctuaries and reserves, often via secondary bottlenecks, resulting in low genetic diversity, low adaptive potential, and inbreeding depression. In this study, we use whole genome resequencing of 30 individuals from the Tiritiri Matangi population to identify the nature and distribution of both SNPs and SVs within this small avian population. We find that SNP and SV individual mutation load is only moderately correlated, likely because SVs arise in regions of high recombination and that are less evolutionarily conserved. Finally, we leverage a long‐term monitoring dataset of pedigree and fitness data to assess the impact of SNP and SV mutation loads on individual fitness, and find that SNP and SV realised load had similar negative correlations with lifetime fitness. However, of the masked load metrics, only SVs had a positive significant correlation with lifetime fitness, indicating that masking of deleterious alleles may be more important for SVs than for SNPs. The results of this study indicate that only examining SNPs neglects important aspects of intra‐specific variation and that studying SVs has direct implications for linking genetic diversity and genomic health to inform management decisions.