Hi Andy
I take it , its the radial crack in the join of the shives that you are worried about, rather than the bits where the filler is falling out.
Personally i'd get some gorilla grip or even PVA glue and work it into the crack gently, wipe all the excess of the surface and leave to dry for a few days, then it should be as good as new. If some dried glue is on the cork once its done, then just rub it off gently (use 800 grit sandpaper if necessary, but only if you have too)
Try to open the crack up a little by pushing the shives on either side, the cork is slightly pliable so should move a little and then spring back into shape
should be no big deal to fix
Hope it helps
Sandy