Treating vinyl cable jackets with oily liquids is a 'double-edged sword' where it may help, but also may speed up the leaching out of needed plasticizers inside the vinyl formulated jacket.
Some peoples sweat is more leaching than others, and only experience with a particular person/cable plastic formulation will one know how much concern is appropriate over a period of years for body contact service.
It is possible to obtain vinyl restoration solutions (like available for water bed vinyl plastic) that especially when moderate heat (short of melting the vinyl) is also applied, greatly helps for driving additional plasticizer deeper into the plastic cable jacket, and this has proven to me a benefit for prolonging the cables flexible service life.
However, if things have gone too far to having portions of the cable jacket split-open, then the tool-handle vinyl brush repair remains only option to at least repair the cable for having a bit more useful service life where the internal copper wire conductors are protected from breaking.