The Best and Cheapest Winch Grease

 
reduce the risk of dropping expensive parts in the sea
An open top cardboard box with taped up bottom edges and a hole cut in it the same size as your winch base diameter.

Pop that over the winch and it'll catch any parts.

For any bowsprit, roller, furler type jobs, an open umbrella hanging under the bowsprit works too.
 
... maintenance instructions are pretty clear about what you _must_ do, and removing the baseplate isn’t on the list.
That said, I would recommend (and have done myself) doing so the first time that you service the winches on an older, but new-to-you boat:
When replacing the thirty year old winches on our first yacht I was surprised by the poor condition of the securing bolts - corrosion, severe deformation, cracking, three bolts were actually snapped off. Recalling that, when we bought another 30 year old boat with the intention of crossing oceans in it, besides servicing all the winches, I also pulled all the base plate bolts and found those to be in an even worse condition.
 
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