Under the assumption you have no file edits
If you do have file edits: reapply those to the new files (from the Changed files package)
in /store: remove install_config.php, any migrationsXXX and io_lock.lock if present (leaving those will retsrat the autoupdate which is what you don't want).
From /cache remove the installer and production folders
use the Changed files package and upload the extracted directories and files
Start the update following the link posted by P_I
the CLI should only be necessary if you have a very large database.
Spelling is freeware, which means you can use it for free.
On the other hand, it is not open source, which means you cannot change it or publish it in a modified form.