I don't think a little bit of grease will hurt anything. If you have soldered the shaft to increase its diameter for a better fit, the lead will be soft. I have used Never Seize grease. The grease would also reduce air leakage along the shaft. Ed
I use "Renolit VLS" from Fuchs-Oil-Company.
It is a very viscous grease that is not soluble in gasoline. A plug of this on the outside of the both shaft ends also prevents any air leakage.