Shift Cable for 1963 Schwinn w/Sturmey Archer Shifter This is the shifter on my 1963-64 Schwinn Racer:

This is the old cable:

I'd like to replace the cable and found this:

It's hard to tell what the cable ends look like inside the packaging but is anyone familiar with this Schwinn part number and if it's compatible with my shifter? I know there are newer style cables with a loop connecting the adjusting nut (ferrule?) to the hub chain, but I'd like to find the older style if possible.
This is my bicycle. There are many others like it, but this one is mine. My bicycle is my best friend. :-)
Based on the information provided by @P.Barney and @NathanKnutson, I realized that while the cable will most likely work in my shifter, the housing is the wrong length for my particular application. Based on the specs of my old cable, I believe the correct cable to be: