I would try the penetrating oil first, and then very carefully try to start it moving back a forth a little at a time.
There is a mixture I make just for this kind of stuff and have a syringe from filling ink cartridges full of it just for small things like that.
50% WD40
25% ATF
25% plain grease (like grease gun grease) then mix them with an allen wrench in my drill.
The WD thins and helps the ATF and grease penetrate.
The ATF also thins the grease and takes longer to dry away.
When both have dissipated it leaves the grease long term.
Works great for hinges latches and window regulator assemblies.