Assign predefined task manually to certain population in Journey

Hello,

Is there a way for the HR to assign manually a predefined task to a certain population of the Journey? For example, the company does not want to add the disability information through a task for all, and they would prefer to manually add this task (questionnaire) to the pending workers that they know they have a disability, through which they will also ask for the appropriate documentation as well:

This is the Add task as an HR that I am referring to, but how can I add the custom task to the drop down list of name? Also, I would like to know if the task is available right after the assignment occurs.