your problem sounds more like bad connection than corrossion. I would never use silicone grease on the battery terminals as it is very sticky and is an insulator - if that gets between the terminal and battery post you will have more problems than you have right now.
A good cleanup and a light coat of vaseline works nice all around the world. grease is sometimes a bit basic but is not recommended as it can eat away the wire insulation over time.
But if that rocks your boat - go for it. Its a regular maintenance item if grease is used.