I would like to cherry-pick a commit on a fetched remote while keeping it's original SHA commit code (my current branch is based on this remote which I resetted to a previous state).
A git SHA hash is computed from different pieces of information:
Even if you edit a cherry-picked commit so that the tree, the commit message, the author and committer information are exactly the same, the SHA of the parent commit (or commits, if dealing with merge commits) will be always different. So, you will not be able to generate the same SHA hash after a cherry-pick (unless you find a SHA collision ;) ).