Since you mention "along the shaft" I am assuming you mean the pump
plunger, not the gasket seal thet envelopes the tire valve.
I have never had them get sticky, but I would recommend you dissasemble
the pump and clean the barrel and plunger as much as possible with
something that won't harm any of the materials. This alone may solve
your problem.
Of course, if lubrication is necessary, be sure to use something you are
sure will not react with any of the components, nor with the rubber of
the tube in case any gets inside during use.
- -
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