Hypoxia contributes to tumor progression and metastasis, and hypoxically dysregulated RNA molecules may, thus, be implicated in poor outcomes. Canine oral melanoma (COM) has a particularly poor prognosis, and some hypoxia-mediated miRNAs are known to exist in this cancer; however, equivalent data on other hypoxically dysregulated non-coding RNAs (ncRNAs) are lacking. Accordingly, we aimed to elucidate non-miRNA ncRNAs that may be mediated by hypoxia, targeting primary-site and metastatic COM cell lines and clinical COM tissue samples in next-generation sequencing (NGS), with subsequent qPCR validation and quantification in COM primary and metastatic cells and plasma and extracellular vesicles (EVs) for any identified ncRNA of interest. The findings suggest that a number of non-miRNA ncRNA species are hypoxically up- or downregulated in COM. We identified one ncRNA, the long ncRNA fragment ENSCAFT00000084705.1, as a molecule of interest due to its consistent downregulation in COM tissues, hypoxically and normoxically cultured primary and metastatic cell lines, when compared to the oral tissues from healthy dogs. However, this molecule was undetectable in plasma and plasma EVs, suggesting that its expression may be tumor tissue-specific, and it has little potential as a biomarker. Here, we provide evidence of hypoxic transcriptional dysregulation for ncRNAs other than miRNA in COM for the first time and suggest that ncRNA ENSCAFT00000084705.1 is a molecule of interest for future research on the role of the transcriptome in the hypoxia-mediated progression of this aggressive cancer.