You’re welcome 
No particular drawbacks in using an external drive when space is at a premium. Just the usual admonition to add the drive to your backups.
Now my question is this: couldn’t I just copy them by drag and drop onto my large external drive? Then I could just run them from the external drivr
Yes, but I’d suggest you make sure to either move the database(s) or remove the copy on the internal drive.
If I now just copy the databases from the internal to the external disk, could that perhaps be a problem for DT, perhaps not being able to find them?
Only if the drive is connected to another Mac without those files.
Or should I simply start from scratch and use File > New Database and save it on the external disk? Then drag the folders I need from the Finder into DT. That wouldn’t take much time, I suppose.
I’d just quit DEVONthink, move the dtBase2 files to the external drive, then double-click each to open them.