x-api-key only secures some resources
Yes, this is possible with a bit of configuration in the AWS console.
In your API Gateway setup you probably have the default resources created with a Zappa deployment: / and /{proxy+}.
You can now manually create a new resource corresponding to your documentation endpoint (e.g. /docs).
Clicking on "Actions" -> "Create Resource" you can create the new resource:
After the resource is created, click "Actions" -> "Create Method" and choose "ANY". Point the method and resource to your Lambda function in the dialog.
By default, the new resource should not require the API key.
Note: you might need to redeploy the gateway before the changes take effect. "Actions" -> "Deploy API".