I was thinking you meant a collar. Support the other end of the rivet on something tough enough then smack it with a centre punch. Turn over and repeat.
Edit: just to clarify, the handle and the blade are solid and not loose. It’s the metal ferrule/end cap that is loose. It’s not going to come off, as it’s captured between the blade and the wooden handle, but it moves.
Bit of a squeeze with, Parallel flat pliers, or a vise with protection from the jaw markings, - but the wood may continue to shrink and will definitely indent - what should be holding it?
Most inclined to live with it unless the fix would be soft
I was thinking you meant a collar. Support the other end of the rivet on something tough enough then smack it with a centre punch. Turn over and repeat.