It's my thought one wouldn't necessarily need a new copy of Win10 when changing the hard drive [HDD or SSD] as the Digital Entitlement/Activation is based on more than that drive. I'd certainly use the MCT [Media Creation Tool] to download and create media to do the install.
Most times changing back to the old drive should work as long as the BIOS still recognizes it. But the question of Why? arises, if only to get old data off of it I'd use an inexpensive portable drive case for the purpose, a lot cheaper than a copy of Windows 10.