Getting rid of cork in a whiskey

My friend got some Signatory Glen Elgin 1991. It tasted quite well, but there's one problem: due to stupid cork design (in combination with rough handling from his side...), tiny pieces of it fell of and is now floating around in the bottle... An absolute nightmare, especially given the steep price of the bottle ($140 over here).

Is there anything we can do except cry over it? I suppose we could filter it, but with what type of filter?

I got a small bottle of absinthe (Duplais Verte, not Czech crap) with the same problem, though I'm guessing the same method(s) could be used for all liquors.