Wharfedale Whizzer Cone Re-Foam
Gordon:
Hi - sorry for the delayed reply. Well, you have called my bluff; I was only passing on hearsay information from memory, and haven't actually done such a repair myself. Upon researching my source for said info, I could only come up with a mention of the subject by a former Wharfedale staffer, as related in correspondence with Troels Gravesen on the latter's website here:
The Wharfedale Super 8/
Now, the quoted staffer does seem confused (failing memory?) about some of the construction details of the speakers under discussion. Be that as it may, upon reading Briggs' writings, it's apparent to me that the R&D at his company was as scientifically rigorous as was possible in those days, with enthusiastic experimentation and listening tests supported by careful measurements. So, if they put foam behind the whizzer cone (a configuration unique to Wharfedale AFAIK), then I would trust that they had good reason to do so, and I would attempt the repair in good faith. I do not have instrumentation to test the results, and would rely on my ears to judge the outcome.
Ok, so - that tiny strip of foam would likely not do much by way of absorption; rather - I think it's function is (primarily) that of damping the free edge of the whizzer cone against breakup vibrations. Hence, I would avoid low-density open-cell foam; instead choosing a medium-density foam that rebounds slowly when compressed and then released. I would try something like "memory foam" or weatherstripping tape. The latter with a pressure-sensitive adhesive backing film might work well, although it might prove difficult to remove without damage to the paper cone in the event you are unhappy with the results. I seem to recall from grade-school art class that rubber cement - if applied to only one surface and left to tack up for a moment - would allow fairly clean removal from paper; perhaps you could experiment with something like that before committing to a more permanent adhesive. (But please DON'T blindly rely on my own failing memory, though!

)
On the subject of meticulous repairs to Wharfedale speakers, I have to also refer "Grumpy's Place" - this fellow documents his obvious patience & love of the craft!
GRUMPY'S PLACE
Anyway, you asked how I would approach this, so there it is... You - or others - may have different ideas, and that's ok with me. Good luck, and please let us know how it goes if and when you decide to tackle this.
Wilf