Highly-doped graphene samples show the conductance reduced and the shot-noise power enhanced compared to standard ballistic systems in two-dimensional electron gas. These features can be understood within a model assuming incoherent scattering of Dirac electrons between two interfaces separating the sample and the leads. Here we find, by adopting the above-mentioned model for the edge-free (Corbino) geometry and by means of the computer simulation of quantum transport, that another graphene-specific feature should be observable when the current flow through a doped disk is blocked by high magnetic field. In case the conductance drops to zero, the Fano factor approaches the value of $F\approx{}0.56$, with a very weak dependence on the disk radii ratio. The role of finite source-drain voltages and the system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape are also discussed.