I just wanted to share this as it may help someone.
I have just taken an Oris Big pointer against another watch, the Oris is complete with its box and some of the paperwork, plus a rubber Oris tyre watch box.
Great.... but the rubber box had gone all "sticky".
I did the usual searches, I tried soapy water, talcum powder, both suggested on the web, neither where very successful, so I have found that Isopropanol (Rubbing alcohol) does the trick.
I simply used an old watch cleaning cloth and after about 15 mins, the "tyre" was back to normal.
I guess it would work for any "rubber" handles or cases.