The surface area wouldn´t affect at all in vacuum, but it will in air.
I can´t imagine that it would not affect in a liquid.
Think of it this way. Using newtons law F=ma
we know that a=acceleration is the derivative of v`(t) where t=time
so m*v`= mg - kv^2 This is usually presented in high school books as a differential equation for free fall with air resistance.
Where k is a constant, and this constant will include surface, shape etc.
v^2 is simply the speed squared.
Actually it does depend on the mass (as well as surface area.) Gallileo's famous experiment at the Leaning Tower of Pisa (which never happened) is not accurate. Two bodies falling in a vacuum have the same acceleration. This has been verified. However if you do Gallileo's experiment and drop two different masses from a decent height you woulld be able to hear two distinct thuds when they hit the ground.
Why is this so? Because the drag coefficient (pick the kind of velocity dependence you wish) does not directly on the mass of the falling object.