Git - rebasing a file into past history of that file

Question

Lets us say I have a file filename in a git repository in subirectory dir1 with a history something like this:

v7 --- v8 --- v9 --- v10

The file is part of a larger repository with various subdirectories, but only the above changesets affect this file. Now I have dug up an old version of that file (filename too) that has by mistake been committed to another subdirectory dir2. This older version only "exists" in one changeset, say:

v4

The problem now is, can I rewrite the history of these (to git) two files so that it appears as if filename has only existed in dir1 resulting in a history something like this:

v4 --- v7 --- v8 --- v9 --- v10

I guess I could try removing the file in dir2 and committing it as a new version of the file in dir1, but that will mess up the actual history of the file so that what is actually the oldest version of the file will appear as the newest.

I have very little experience with "tweaking" the history of git repositories, so I do not know how to do this, but I am guessing rebase may be the answer? I am the only one working on the repository, so my only concern will be sync'ing these changes across two computers.

I guess what I want to do is really just leave the file originally in dir2 where it is in the history, but I want to change the commit called v4 above to make the file a version of the file in dir1.