Soft Touch Removal
Soft Touch is a coating applied to plastics to give them a soft grippy feel. This maybe useful when the product is new but overtime this coating becomes sticky mess that is anything but nice to touch.
Once in this "sticky touch" state removing it can be difficult. One method is to scrape it off with a finger nail or other soft scraper but this is very slow, even for small items. The coating resists most solvents but Methylated Spirits and a cloth or non-scratch scourer will shift it. It is still a long process though.
There are two layers the nasty rubbery stuff on top and a firmer paint like film underneath. Petrol is slightly better on the film than Meths. For both make sure your cloth is reasonably wetted with meths and possibly leave the cloth in contact for a minute or so helps.
Once cleaned with meths, wiped over and dry the plastic can look a little grey or faded. Use a mild mild abrasive/polish usch as Brasso or a uPVC Reviver, the latter has things in to soften the plastic and thus help fill scratches which will help restore a shine and lustre. After polishing wash any residue off with detergent and warm running water. To further fill and seal the abraded plastic surface apply a little bit of silicone furniture polish via a paper towel.
Other solvents that might be worth a try are liquid lighter fuel or a limonene based cleaner. Lighter fuel might be too volatile to be easy to work with, it may evaporate faster than it lifts the soft touch gunk.