Yes. You can copy the entire Bitcoin Core datadir from your internal drive to the external drive. You will have to always start Bitcoin Core with the -datadir option so that it knows where to look for the datadir though.
What do you mean with the datadir? I am not familiar with all these therms.
To find your datadir, open Bitcoin Core and go to Help > Debug Window. In the Information tab, you should see a field labeled "datadir" and a file path next to it. That path points to the datadir. Cut and paste that folder to your external drive. Then stop Bitcoin Core and start it with the -choosedatadir option. See https://achow101.com/2016/07/Bitcoin-Core-Troubleshooting#option-startup for help with that. That option will open up a dialog for you to choose your datadir. Choose wherever you put the datadir and you should be good to go. Starting with that option only needs to be done once.
