You can unlock your macbook air with the acr122u reader. There is a software for iOS for the reader - but I wasn’t able to install it. At the app store on your computer there is an app called NFC Ideas.
In the end of february we will get an apple store in Vienna. I will go there with my macbook and the reader, maybe they can install it.
Maybe you can get a cheap android phone for writing. My Samsung S8+ works also perfect with my macbook 
no problems.
Greetings from Austria