Mechanical manipulation of DNA, by forced extension, can lead to a structural transformation of double-stranded DNA (dsDNA) from a helical form to a linear zipper-like form. By employing classical molecular dynamics and quantum mechanical non-equilibrium Greens function-based transport simulations, we show the ability of graphene nanopores to discern different dsDNA conformations, in a helical to zipper transition, using transverse electronic conductance. In particular, conductance oscillations due to helical dsDNA vanish as dsDNA extends from helical to zipper form as it is transported through the nanopore. The predicted ability to detect conformational changes in dsDNA, via transverse electronic conductance, can widen the potential of graphene-based nanosensors for DNA detection.