I wonder if Simple Green might work good for gumwalls. Be aware that the gumwall material can dry out and deteriorate just like gum brake hoods. The gumwalls on my old Specialized turbo VS turned to dust........but that's after about twenty years of storage and non-use.
I had success cleaning my old Peugeot's brake hoods using mild cleaners/polishers like Pledge. I don't think it's non-wax formula wil make a tire's tread slippery, but you might have to test it on an old tire you're ready to throw out already it to find out.

Chombi
84 Peugeot PSV