Usually, you have to make an unsubscribe link go to a website that handles your mailing list. Personally, I do it myself; my unsubscribe link takes you to a page on my website. That page registers your unsubscribe in a database and marks your email address not to be sent. I don't know of any way that you can do that without that kind of service, unless the person replies with "unsubscribe," which used to be the norm back in the day before web pages were popular. The receiving mail server could process the unsubscribe, but I haven't seen that done in years. So, to answer your question, you do need a service to do this, or you can build it yourself if you know how to do it, like I don't - my own.

With nothing other than access, I'm pretty sure you're going to need more or have the respondent manually respond to the email and have you remove them. If you have an online domain you can probably setup an ASP page behind the button to accept and have people go to a link when people push the button and have them unsubscribed

I guess I'm slow typing today, what Richard said lol