You do not need to register the notebook to purchase a battery for it. Registration has al;ways been optional, except in order to have and use the warranty.
The description and part number for the compatible battery:
47 Whr, 2.20 Ah Li-ion battery HP p/n 593553-001
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For laptops or desktop PCs, use the Fn+Esc keystroke while logged into Windows to locate the Product number (SKU)
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