Is there way to scan a registry hive on an attached USB drive?

What you want to do is called 'offline registry editing'. You can load the registry hives from the old hard disk drive into your registry editor. Here's a tutorial:

Load registry hive for offline registry editing

However, I'd recommend to use BartPE instead of your current Windows installation to do this:

How to edit the registry offline using BartPE boot CD?

BartPE will recognize your external USB hard disk drive connected.

Personally I recommend backing up the old disk and then wiping it

This way you don't have to worry about the virus remaining behind and it's more efficient too.

Note: the problem you're having right now is probably that the host OS (you're using right now) doesn't have access to the Windows folder of your infected guest OS. Using a Linux Live CD would allow you to "ignore" these permissions and restore whatever files you need.

Alternatively you could use a virus scanner within Linux to scan the drive as well, but I'm sure a clean install will give a better and more efficient result