In general, when adding a node to the cloud server, you don’t have to copy any key, the procedure to add the node will propagate the key for the node to use. To do that, you need the admin credentials on the node, the Terminal Server host in your case.
However, when you don’t have admin permissions on the node you want to add, for example there are two separate administrators for both machines, you can indeed pass the CS public key to the admin of the TS Node, and they can place it in the appropriate directory. On Linux, the public key can be found in the directory, for example in /usr/NX/etc/keys/node.localhost.id_rsa.pub. You, the CS admin, can then proceed to add the node to the Cloud Server with sudo /etc/NX/nxserver –nodeadd IP_of_node –node-name name_of_node.
See the article here: https://www.nomachine.com/AR11V01258.