Sounds like you need some vise pads to hold your stave without much pressure. You don't have to clamp the splice in the vise, you can clamp the fade area.
I use these, easy to make, easy on and off.
I highly recommend a post to support your stave while you work, this will minimize the pressure you put on a stave while it is in the vise. This is an old picture with cheap magnet vise pads, they worked poorly.
Another thing, the glued area of your splice is a lot stronger than bare wood, it is highly unlikely vise pressure will harm it.