Sturmey 3 speed pulley/cable... ?

[ParkRNDL]

I want to convert the 3 speed thumb shifter on my Speedster/Manta project to a top tube stick shifter. The original cable has a plastic-looking cover or coating on the exposed part where it's not inside the cable housing. I assume this makes it run smoother with less wear on the jockey pulley. The cable I have attached to the stick shifter doesn't have that. Will it damage the jockey pulley to use a cable without the plastic cover?

For what it's worth, this is the shifter I want to use:

(please ignore the hack job I did mounting it on this twin-tube Ross... )

 

[Wildcat]

I've replaced old coated cables with new bare cables several times and they don't hurt the pulley. Just make sure the pulley turns freely. The coating was mainly for rust prevention probably.