Ballistic graphene samples in a multimode regime show the sub-Sharvin charge transport, characterized by the conductance reduced by a factor of /4 compared to standard Sharvin contacts in two-dimensional electron gas, and the shot-noise power enhanced up to $F\approx 1/8 $ (with F the Fano factor) [Phys. Rev. B 104, 165413 (2021)]. Here we consider the disk-shaped (Corbino) setup in graphene, with inner radius and outer radius , finding that the multimode conductance is slightly enhanced for any < , reaching (4 − ) 0.8684 of the Sharvin value for . At the same limit, the Fano factor is reduced, approaching (9 − 28) / (12 − 3) 0.1065 < 1/8. Closed-form approximating expressions for any ratio are derived, supposing incoherent scattering of Dirac fermions on an asymmetric double barrier and compared with exact numerical results following from the mode-matching method. Sub-Sharvin values are restored in the narrow-disk limit 1. For experimentally accessible radii ratios 0.5 0.8, both the conductance and the Fano factor are noticeably closer to the values predicted for the limit, yet still differ from standard Sharvin transport characteristics. The system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape is studied numerically and the crossover from the sub-Sharvin to standard Sharvin transport regime is demonstrated. Implications for a finite section of the disk are also discussed.