I think I read that connecting an Amiga drive to a PC will corrupt it.
Only if you run Win95/98/ME. Win2K/XP/Vista will not currupt the drive (unless you tell it to do so).
Is there a way to make an exact copy to a new(er) hard drive?
Only if the new drive is exactly the same size as the old one. There is no software to change partition sizes. Windows software won't even see any partitions on an Amiga drive.
The better solution is to just copy all files from the old hdd to the new one as was already suggested.
Bye,
Thomas