How do I lube a clutch cable.

83 honda shadow vt500c.
The clutch cable was making a squeaking noise, so I decided to lube it.
Over the course of several hours, gravity managed to get a few drops
of oil down the cable.
Doesn't squeak any more, but I have a new symptom.
Don't know exactly how to describe it. The friction changes over the
range of movement sorta periodically.

Now what?
The cable won't come out of the sheath. How do I get something as thick
as wheel bearing grease down there.

It would be relatively easy to pull a vacuum on the bottom end, but will
15PSI negative suck in grease?

Or machine a clamp that covers the end with a Zerk fitting on it.
I was gonna make the cavity big enough to enclose the knob on the end
so I only have to seal one end.
Should be able to get plenty of force that way.

I did find such a clamp on the web, but it's designed for thin spray
lubricants. No option for anything thicker.

Should I be attempting a different lube? It's an old cable, but I really
don't want to spend any more $$ on this thing than I have to.

Ideas/tricks?
Thanks, mike

Motion Pro makes a good aftermarket cable for this bike- retails for
$12. It's a no brainer.