As Rubén said with the Trigger class you should be able to do it through code, but it is possible that it gives you problems. (mainly that sometimes does not fire)
Right now I do not know how the issue is but a while ago at least it was advisable to use manual triggers since code triggers do not go well. (I do not know if today this part has been fixed / improved)
I disagree with Rubén (sorry :) about the addon since the process of publishing an addon is quite heavy (there are quite a lot of quality filters that are totally logical but that complicate the process too much) and it does not make much sense being a script for inside a company (I understand that the script runs on the domain of the company, so it does not matter if it is public, as it should be with the addon)
By cons I would recommend another option: Have a single trigger in your script. Can you explain more or less and without details what your script should do? Do you need permissions for each user? It depends on what you had to do, maybe it would be worth having your trigger in your master script and processing the information of the users that have registered.
When I schedule scripts for my company (and I do it daily :) I always try to make users users and not owners of the script. So you have everything centralized, you facilitate the correction of bugs and control the permissions better.
If you give more details of what your script has to do refine my answer a bit more.