2-butoxy ethanol ("Butyl Cellosolve" and several other names) plus a base such as ethanolamine are common ingredients in household cleaners, including strippers for acrylic floor wax. Diluted in water per label directions, it is safe on vinyl and many plastics. The American brand I use is ZEP, but its active ingredient formulation is not unique. I use it to remove soldering flux fro PCB/s. It will remove many paints but does not seem to affect the silkscreen on PCB's.
While TSP will probably work too, it is restricted in some area. Sodium metasilicate, which is also very alkaline, is sometimes used as a TSP substitute.
If the cases have painted labels, be sure to test on them. (I am sure you know that.)