Risks when cloning a drive

I'm running Bitdefender AntiVirus for Mac and also have a Bitdefender Box 2.

I need to access the contents of a hard drive that came from a computer that was mostly unprotected for a long time. My first move was to do a full scan on that drive with BD. The scan found and removed some problems. I'd now like to clone the drive to an SSD to make it easier to examine.

Is there any danger to the host computer when cloning a drive? Does the cloning process simply move data or does that data temporarily live on the host during the copy? If, hypothetically, there was some problem BD didn't find, could it affect my computer?

I'll be using either of the primary Mac cloning tools -- Carbon Copy Cloner or Superduper.

I imagine this is a pretty paranoid question, but I appreciate any light anybody can shed,

Steve