Is using email outreach for website traffic blackhat SEO?

I have an email campaign with a 35% open rate.

The people who i send these emails to are usually very happy and eager to communicate with me further, even going so far as to email me a few times out of the blue.

Looking at my website im seeing a spike in traffic and I credit that to the email outreach.

The people i emailed took the time to search my company and look up the email.

Now if I were to link my website on the email with a button that says [learn more], would this be unethical?

Try to add button to a smaller group of people and see how they behave.
If everything is fine you can send it to everyone