In fact avoid any payware registry cleaner/registry defragger/defragmenter for the file system - all are available for free and these will do the same job.
If you want a free online registry cleaner, then use the windows live online tools- free registry cleaner is included in the kit.
The registry cannot be "healed".
But it can be cleaned by reg cleaners.
Use the ccleaner you downloaded and installed - it has the basics and does a decent enough job. And it is freeware.
There are other freeware registry cleaners to add and use to this, but the least of your concerns is cleaning the registry - your main concern is removing the malware.
I will give you some other additional registry cleaners to use, but use these later and after using the ccleaner for a few times.