She's probably got it in a nice display box in her ready room or quarters just slightly off-camera.
My point. When Sisko made a clock in an essentially mediocre DS9 episode, the clock was on his desk afterward. When Kathryn received a watch in the best VOY episode ever, it's never referenced again. Even though it should have been, for aforementioned reasons.
Alternatively, Chakotay might have felt brave enough to give her an elaborate gift that showed how much he cared for Katheryn in the "we're all gonna die" timeline, but maybe in the reset timeline without those events happening he chickened out on giving her something so special.
Very possible.