There is currently no way to batch edit the location of attachment files. There have been several requests for ways to manage attached files in this kind of fashion but I don't think there is any proposed resolution.

I know, it's not recommended but would this be possible with a third-party sqlite client?

On Windows or Linux, yes, you could do it with the SQLite REPLACE() function. On OS X, no, not the way linked file paths are currently stored, though we'll likely be changing that.

Any suggestions on the exact command?

Something like this should work:

UPDATE itemAttachments SET path=REPLACE(path, 'C:\Path\To\Old\Dir', 'C:\Path\To\New\Dir');

You'd want to make a backup copy first, of course, and I'd also recommend doing a SELECT first to make sure you'll be getting what you expect:

SELECT path AS oldPath, REPLACE(path, 'C:\Path\To\Old\Dir', 'C:\Path\To\New\Dir') AS newPath FROM itemAttachments;

given that 4 years have passed since the last post in this thread, you may want to look further.

I think zotfile will do this for you.
http://www.columbia.edu/~jpl2136/zotfile.html

You probably want to use Zotfile for this. It accomplishes this sort of movement without messing with the SQL.