Dwarf galaxies are excellent cosmological probes, because their shallow potential wells make them very sensitive to the key processes that drive galaxy evolution, including baryonic feedback, tidal interactions, and ram pressure stripping. However, some of the key parameters of dwarf galaxies, which help trace the effects of these processes, are still debated, including the relationship between their sizes and masses. We re-examine the Fornax Cluster dwarf population from the point of view of isomass-radius-stellar mass relations (IRSMRs) using the Fornax Deep Survey Dwarf galaxy Catalogue, with the centrally located (among dwarfs) $3.63 \mathcal {M}_{\odot }$ pc-2 isodensity radius defining our fiducial relation. This relation is a powerful diagnostic tool for identifying dwarfs with unusual structure, as dwarf galaxies' remarkable monotonicity in light profile shapes, as a function of stellar mass, reduces the relation's scatter tremendously. By examining how different dwarf properties (colour, 10th nearest neighbour distance, etc.) correlate with distance from our fiducial relation, we find a significant population of structural outliers with comparatively lower central mass surface density and larger half-light-radii, residing in locally denser regions in the cluster, albeit with similar red colours. We propose that these faint, extended outliers likely formed through tidal disturbances, which make the dwarfs more diffuse, but with little mass-loss. Comparing these outliers with ultra-diffuse galaxies (UDGs), we find that the term UDG lacks discriminatory power; UDGs in the Fornax Cluster lie both on and off of IRSMRs defined at small radii, while IRSMR outliers with masses below $\sim 10^{7.5} \mathcal {M}_{\odot }$ are excluded from the UDG classification due to their small effective radii.