Animating a sword swing

I have a pre-rigged pair of arms (just floating arms), with the IK already setup. I'm trying to create some animations where the right arm holds a sword and swings it in a few different ways. I have the sword parented to the hand bone, and I'm animating the hand IK and the forearm rotation mostly to do the swings. But none of the animations are turning out right, no matter how much I struggle with them. In particular, one aspects is frustrating me:

making the sword swing actually follow a straight path - it keeps shifting slightly and rotating in between keyframes, making the path weird. I understand that this is probably because of the way the IK is setup, the bones are all shifting in subtle ways as the IK position changes over the interpolated frames, but the question then is how do I get over this?

I've tried searching tutorials online for how to animate something like this, but I mostly find sword trail effect videos. Was wondering if someone here has tips/tricks/workflows/suggestions for improving this.

I'm using blender 5.2, and this is the pre-rigged pair of arms I'm using. It comes with a .blend file which I can open and edit stuff in.