a way to reset the counter numbers
Not easily. I don't see a way to do other than reset it within the software. And it wasn't even easy to track down how CC4 stores the data. I had to use process monitor to trace it.
The counters are stored in a binary file:
C:\Users\<YOURACCOUNT>\AppData\Roaming\ControlCenter4\<YOURPRINTER>\CcScanKey.dat
You could try to copy the file, do a scan, do another copy and look at which bytes are incremented. But it's probably more trouble than it's worth.
Or, actually, now that I'm thinking about it, you could try and copy the file over from the old computer to the new one.