How do I modify redshifts to gain corrected line of sight velocities?
You need a model for the motion of the Sun with respect to the Milky Way centre. You then have to subtract the component of this that is resolved towards the galaxy in question.

The solar motion around the Galaxy is somewhat uncertain, but is roughly (11, 240, 7) km/s when expressed as a vector aligned with Galactic coordinates (i.e. towards the Galactic centre, tangential to the Galactic centre and perpendicular to the Galactic disk).