is it just "Deactivate, Delete, Download New Version, Activate"?

or is there a quicker way to do it on Nexus?

With the Nexus, you should be able to download the new version of the mod and install it, you'll get a prompt to deactivate the older version or old files will just get overwritten. You're generally right, though, but I'd strongly recommending reading the install/update instructions every time just to be sure. Some mods have more specific update instructions, and sometimes they even have a faster way (like mods that add several GB of new data, updates can generally just include the updated plugin and new files for a faster download).