Our aim was to identify the suitability of three assessment tools (i.e., Flanker test, Updating Word Span, and Color Trails Test) for future inclusion in the classification process of elite Paralympic athletes with intellectual disability and to assess the strength of the relation between Executive function (EF) and intelligence. Cognitive and EF assessments were performed on 59 participants, divided into four groups according to their cognitive level (with versus without intellectual disability) and sport expertise (athlete versus novice). Inhibition and working memory update skills were implicated in people with intellectual disability. For set-shifting, a more nuanced picture was observed. Strong associations between EF and intelligence was found in people with intellectual disability. Working memory updating and set-shifting are relevant EF skills to assess in the context of elite sport; however, culture-free alternatives for the Updating Word Span test are needed, and alternatives to the Color Trails Test, less reliant on literacy skills are required.