as far as I understand you had an account, but you can no longer log into it? Did you try to reset password, so you can access/delete your alerts? It would be the easier solution.

Alerts can be created only if you are logged in and yes, it is possible to put a different email address for receiving alerts, than your Windy account is under.

My advice would be to restore your original account and delete the alerts there.
Or if you have a different account now, you can still delete alerts through the link in the alert email - 'Edit / Unsubscribe'.