Modifying the SKSE archive is not something that is intuitively obvious, or something I would recommend.
Modifying the skse archive is a waste of time, since regardless of how you pack the archive the second Vortex extracts the data directory it is removed, meaning you can never install both exe + script without either change Vortex to correctly handle this, or you must manually move the files around yourself.
Now if you split skse into two separate archives on the other hand with one only containing scripts and the other the rest re-archiving can work.
While you can install scripts from original skse archive, if you tries the same with exe Vortex always screws up by putting exe + dll into a sub-directory. Now some will say skse is not correctly packaged, but this is nonsense since it is Vortex that isn't correctly extracting and installing the files, meaning it is Vortex that needs to be fixed.
At the moment the best way to install skse in Vortex is to extract skse directly to the mod staging folder, re-start Vortex, and after Vortex detects the new mod change to dinput.
Some of the advantages of installing at least the scripts with a mod manager are, conflicts with other mods are shown and you can easily make sure a mod using an outdated skse script is overwritten, updating skse makes sure all scrips are new. Also if you're looking for any non-managed files left over in data directory, by purging the installed scripts will be removed and you don't need to waste your time checking the scripts are from skse.
Since Vortex can also manage exe + dll + anything else going under root and not under data, it is very unfortunate Vortex makes this unnessesarily complicated. One way to improve things would be if it was possible to select dinput before installing the mod and in this case change Vortex to not delete data and not put exe + dll into a sub-directory on installation. Alternatively Vortex could auto-detect skse and correctly install + automatically choose dinput.