Is there any danger to relaunching Finder while external drives are connected? I tried to do a very large copy (2TB) by copy/paste to two external drives. It hung up on the "Preparing to copy" dialog. After about 20 hours of waiting, I cancelled and that also seems to hang.

Can I unmount these drives, and/or can I relaunch Finder without worry to the data on the drives?
You can relaunch Finder without any worry, yes. Relaunching Finder won't unmount/remount the drives or anything like that. The copy operation you had started would be cancelled though.

Whether or not you can directly unmount the drives depends on whether any programs have files open on the drives. You would need to close those files (or the programs) before you can unmount the drives properly.