I have a 63 dart with the pushbutton tranny - What tranny is it - the 727 or the A 904 (or is it something else)? I want to get the right kickdown linkage when I get my 2-bbl carb.

It most likely is the 904. The transmission won't matter with the kickdown linkage. Your difficulty will be in overcoming the rod style throttle linkage.

I wonder if I could leave the kickdown linkage the way it is and hook up a universal cable to the pedal or something. . .

Look at how the gas pedal actually operates the throttle. There isn't any easy way to retain just 1 piece of the factory setup. The easy way is a floating pedal from a later car and the lokar kd linkage.