there's no specific function for what you want to do, you have to rely on existing ones, but there's more than one way to go.
my suggestion: make the protected folder as usual, with permission for the account. Let's say the folder is named "myfiles".
Then re-add the folder to the virtual file system, this time it will have a different name, like "myfiles-give", but it points to the same folder on the disk.
This instance of the folder shall not be protected, but you remove the "browsable" flag. (under properties > flags)
Now when you want to give away the file you just uploaded, copy the link to it and pasting modify the url by adding the -give to myfiles.
People will access the file unprotected, but only those who have the direct link to it, others won't find it because the folder is not browsable.