Git pull without fetch

[ronan@rjp.ie]

Dear maintainers,

I use the git-maintenance prefetch task with a certain repo to periodically
fetch updates from the remote. I'm trying to figure out a way to have git
"complete" a prefetch on command, via an option, alias, or other extension that
mimics the behavior of git pull, but does not fetch from the remote. By
comparison, `git pull` or `git fetch && git rebase` would fetch the remote and
fast-forward my local copy to match, but I don't want to fetch the remote.
Instead I want to fast-forward my current branch (and the remote tracking
branch) to the prefetched tip as if git pull had been run at the time of the
last prefetch.

For example, suppose my local copy has a branch master that tracks the remote
branch master from origin. Suppose that the local copy (and the remote tracking
branch) have commits A--B, the remote has commits A--B--C--D, and commit C has
been prefetched and is pointed to by refs/prefetch/remotes/origin/master. The
desired effect could be accomplished, I think, by:

git update-ref refs/remotes/origin/master refs/prefetch/remotes/origin/master refs/heads/master &&
git rebase origin/master master

My question is, how can I calculate the correct remote tracking branch to
accomplish this operation in the general case, just as git pull without argument
would have done? Or is there a simpler way to achieve my goal?

Cheers,
Ronan