I usually would do this as an automation as it is simpler and easier to maintain and edit.
Automation would be:
- Query - Suppression list
- Email Send
The query would be there to gather your link clicks for 'Stop receiving the reminders' from your email/landing page. If you are using API from the landing page, this step can be skipped.
You can gather these link clicks either through API (REST or SOAP) on the landing page (or AMPscript/SSJS if hosted on SFMC) or if it needs to be based on the click in the email, you can use the _Click dataview to gather this info.
Sample Query:
SELECT SubscriberKey
FROM _Click
WHERE LinkName = {{YourAlias}}
To use the Click query, it would be best to utilize an 'alias' on the link and then use that in a where statement. If this is not possible, you can try to query based on URL or some other unique identifier for this link.
Whether through the API or Query, you would then put this information into a DE that would act as either a suppression or exclusion list inside your User Initiated Send.
This way it will not unsubscribe the person in any way (which I believe is your goal), but it will prevent that person from receiving any more of these messages.