essentially all mechanical corkscrew will involve twisting and/or pulling.
a "double acting corkscrew" - go google - eliminates the pulling bit, but not the twisting 'screw in the corkscrew' bit.
foil cutter? those are pretty simple - squeeze and rotate bottle... is that going to be an issue?
an option with no twist&shout action is the "poke it in, press button to release CO2" style - you given the cork an injection and use CO2 pressure to pop the cork out.
note: these work peachy keen with natural corks; not so much with the plastic neo-corks. sticking the needle thru a plastic cork requires a lot of muscle....