Once you can connect each computer to the Internet without re-cabling, you have established a pathway that can be used for this Migration. A mix of Wi-Fi and Ethernet connections can be used, but most Wi-Fi connections are slower.
The most trouble-free way to use Ethernet cabling for this migration is to connect BOTH devices to your Router with Ethernet cables, even if you have to carry one or both over next to your Router.
The connection through your Router will be a local connection (through the Switch portion of the Router) not actually using the Internet-connected portion of your Router. But setup is much easier when the Router sits in the middle and supervises.