I'm not sure what you'd need to do to disconnect your fork, but clicking the "fork" button will often get your repo automatically taken down if the parent repository gets DMCA'd.
If the commit history is different (say, because you rebased the project onto a slightly different initial state), Github won't auto-detect the fork as easily, so the lawyers would need to find your project and include it in their takedown notice.
It could still be identified as the same codebase by eg. comparing commit hashes or content hashes, but that's harder. If you really want to be sure, clone the repository, make a few local edits to files (eg. adding a comment to each file), copy the full source repository to a new directory in the filesystem, git init that as a new repository, commit changes, and push. That blows away all the existing history of commits, and ensures that each file has a different hash. It's still technically possible to detect it as a dupe, but would require an extremely expensive shingling or filesystem diff on every repository in GitHub.
Wouldn't a GitHub search still find it pretty easily? As I understand it, they put significant effort into supporting search; but since that's being done anyway, it doesn't have a very high marginal cost.