A simple Finder copy will capture most invisible files -- if you copy a container (folder/disk icon), Finder copies the contents. Exceptions might be the desktop files so you would lose application/file type associations if that was the case. However during the 25+ years that I have been backing up drives in this way (just dump HD contents onto a server or portable drive), I've never hit a serious problem.

Or StuffIt. Again, you will probably lose the desktop files but you can always back them up separately.

SunTAR was an early backup utility that used low level disk access to copy disks. Mirrors of the old Info-Mac and SUMEX archives should throw up alternatives.