Do the one-sheet Savage Worlds adventures only require the core rules, or do they generally use some setting-specific rules?
Just the core rules is fine. For that matter you could probably get away with using the Test Drive, given they also provide pre made character downloads.
You might need the setting supplements for fluff information, depending on how detailed you want to run it, but that really shouldn't be necessary. I always used to run adventures from Dungeon which I didn't have the campaign setting for.