Wouldn't necessarily go with a solvent
What type of seacock is it?
On traditional Spartan and Wilcox-Crittendon seacocks, there are 2 nuts opposite the handle that can be loosened to make it easier to move the handle. I like PB blaster to loosen corrosion. Last winter, I unfroze 15 stuck seacocks. If you are on the hard, you can take the seacocks apart, clean them with mineral spirits, use lapping compound to smooth them out if needed, and lubricate with grease.
If these are ball valves, I haven't worked on those.