How can I secure an Air Tag?

It will depend on how secure you want to make this tag. I would think the 3M tape would be the best choice, but duck tape could work. I definitely do not recommend super glue or any taping method that completely covers the tag.

The tag utilizes a Bluetooth beacon to transmit its ID to the Apple Find My network ... which literally is comprised of millions of other iPhones. Also the tag's speaker is built into the metal battery cover, as well as, this cover is how you access the tag's battery when you need to replace it.

Finally, be aware that the tag's Bluetooth signal could interfere with your Bose headphones, if those headphones also rely on Bluetooth.

3M, maybe other brands, offer double-sided "sticky" tape that you can try for this purpose. They have one type, known as command strips, that are designed to be easily removed when you want to separate the tag from your headphones.