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Though smooth, extended spheroidal stellar outskirts have long been observed around nearby dwarf galaxies, it is unclear whether dwarfs generically host an extended stellar halo. We use imaging from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) to measure the shapes of dwarf galaxies out to four effective radii for a sample of dwarfs at 0.005<z<0.2 and 10^7<M_star/M_sun<10^9.6. We find that dwarfs are slightly triaxial, with a <B/A> >~ 0.75 (where the ellipsoid is characterized by three principle semi-axes constrained by C<=B<=A). At M_star>10^8.5 M_sun, the galaxies grow from thick disk-like near their centers towards the spheroidal extreme at four effective radii. We also see that although blue dwarfs are, on average, characterized by thinner discs than red dwarfs, both blue and red dwarfs grow more spheroidal as a function of radius. This relation also holds true for a comparison between field and satellite dwarfs. This uniform trend towards relatively spheroidal shapes as a function of radius is consistent with an in-situ formation mechanism for stellar outskirts around low-mass galaxies, in agreement with proposed models where star formation feedback produces round stellar outskirts around dwarfs.