Bow sway should just be a script that alters the crosshair position. Shouldn't interfere with animations at all.
So, all the animations are placed in "\Oblivion\Data\Meshes\Characters\_male", and you have no changes at all in third person view?
well I don't use bow sway, so I was unsure about that one...I thought it literally made the player move the bow (ever so slightly) in a sway to throw off aiming a little.
anyways...good point, I was looking at folder structer and realized there is the "optional" folder for first person animations. If you didn't plug those in as well (and playing in first person), that could be the cause.
if third person is too hard to aim with(due to camera position), I highly, HIGHLY recommend http://www.tesnexus.com/downloads/file.php?id=29942. It doesn't work well with Deadly Reflex's animations, but the fix it does to the Third Person camera is worth it.