I don't think there is a perfect answer, so you may have to choose the imperfect answer that seems better than the others.
I can think of the following options:
Make confirmation a pre-requisite for email notifications (this is by far the most sensible, but seems counter to your question).
Have a captcha when requesting notification to reduce abuse - I'd advise against this, it is awkward for genuine users and does not prevent entering someone else's email address. It might however reduce abuse by spam bots attempting to post comments to your site whilst using a made-up or borrowed email address.
Hope that it isn't abused - you could assume people are unlikely to enter someone else's email address (why bother?), and include a link in every email to turn off further notifications. I'd also advise against this, as it might get your sending address spam-listed if people keep junking your emails.
I'd suggest you limit the number of notification emails you send out, and do some monitoring. Make sure you aren't sending 100s per day to one email address. If you get spam comments, maybe block the associated email from all notifications. If notification emails are being ignored (i.e. links are never clicked), then you could stop sending to the associated address. Also make sure you don't attempt further sending to non-working email addresses.