Boot from a Win10 installation DVD or USB flash drive and you'll be able to reinstall. Just make sure you use the same language, type (as in Home or Pro) and bit-ness (32- or 64-bit) as you have installed.
Your plan to copy drives may work provided the installations were the same types as above - Win10 activation relies on "digital entitlement" stored on MS servers, not serial numbers/keys so the fact the hardware has had Win10 previously installed means it's "entitled" and doesn't care that the drive is from another laptop. FWIW I've successfully transferred a Win10 drive from HP to Lenovo.