This is the exact opposite of the truth. An edge-on spiral galaxy without dark matter would have less extreme observed rotation velocities (comparing the blueshifted and redshifted sides of the disk), because only the visible mass (stars and gas) is relevant. But in practice we see higher rotation velocities (greater difference between blueshifted and redshifted sides) than can be explained by just the visible mass, and so we have to postulate extra mass in the form of "dark matter" in the galaxy.
(Dark matter halos are not just dark matter outside the visible galaxy, they extend all the way to the centers of galaxies, and in fact become denser the closer to the galaxy center you get. Of course, the visible matter also becomes denser the closer to the center you get, and usually faster than the dark matter does, so the central regions of massive galaxies are dominated by the visible matter. But there's still dark matter there, and in some dwarf galaxies, the dark matter even in the central regions.)