Can I set a particular sorting option to be default for a specific category only?

Yes, this can be configured in the Category Display Settings. Please navigate to Catalog > Manage Categories, select necessary Category from the category tree, open the Display Settings tab, uncheck the ‘Use Config Settings’ checkbox and choose the sorting option you’d like to set up as default for this category in the ‘Default Product Listing Sort By’ field:

Magento Improved Sorting - Amasty

See more details on Improved Sorting page
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