Yes, Buxfer is designed to work even if you can't or don't want to sync your bank accounts.
You can use one of these methods to enter your transactions:
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Upload statements: Download statements from your online banking website and upload them to Buxfer.
Read more here.
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Manually enter transactions: Manually enter transactions one at a time. While more tedious, this is also
more flexible and allows you to enter future-dated transactions, itemize transactions, etc.