JHQ Dansk Congo Ice bucket - plastic liner replacement  

I believe there is also an insulating shell between the staved teak and inner plastic liner. One of my three buckets has a broken insulating shell that you can hear (but not see) rattling around every time you rotate the bucket.
I think trying to find separate insulating shell and inner liner, then trying to fit them into the bucket around the handle without damaging them, then have a clean fit at the rim, might be more trouble than it's worth. My guess is that the handle was installed in the factory after the two liners were inserted.
I'd recommend keeping it without the liner for a show piece, then buy another one with the liner if you actually wanted to use it for ice cubs or chilling wine.