Shifter Knob Removal Situation

You don't say what year you're working with, but, if the push button knob is metal, and you don't mind rechroming it, you could try hitting it with a torch. If it's a plastic button, it will melt, so, you'd have to replace it, but it will save having to replace the cable. Otherwise, maybe pull the shifter and console assembly out together and flip it up side down so the shifter knobs can be dunked in a bucket of penetrating oil? I think I'd just drill out the button to get down to the cable connection and get a new button. Good luck!