You will want to run the “Airtable” interfacing part of your app on your server.
Since you are using Javascript, I assume you Node.js will be your choice of language.
After that make calls from the client(browser) using Ajax, or some other javascript framework like Angular etc to your server (described above) and NOT to the Airtable API directly.
Thus your API keys will be hidden since it will be running on your server, to which only you have access to.