If you're only concerned about the motion of the object, not it's actual energy. You can toss the mass out of the equation and use specific energy per unit of mass
. You can also toss out rotational kinetic energy.
You can do the same with the angular momentum. You want specific angular momentum per unit of mass
. For trajectories, your specific angular momentum is the cross product of the radius and velocity vectors.
Something has to be given. Since you're talking about hyperbolic orbits, you want E to be some value greater than 0 (If E=0, you have a parabolic orbit; if E<0, you have a closed elliptical or circular orbit).
Your max velocity is going to depend on the lower limit you set for r (there's some point where r is smaller than the central mass's radius).