Are you referring to this Shopify App: Ship, Rate, and Track for FedEx?
And may I know which country you are from?
The $19/month charge is for using this app to integrate FedEx with Shopify and using features like displaying live rates, generating shipping labels, managing the packaging process, requesting carrier pickup, print manifests, and track orders. You need to have your own FedEx account to integrate with Shopify and, you will be charged per label by FedEx whenever you generate shipping labels.
In order to integrate FedEx web shipping tool to Shopify store, please let me introduce Ship&co application to you. Basically, Ship&co will only charge you per label, no additional services or support fees, starting from $0.25 each and cheaper when you print more labels.
Ship&co is the official compatible solution for FedEx (and we're also Shopify seller, using this app to manage FedEx shipment for Shopify store). You will have no concern since Ship&co supports FedEx Electric trade document, Delivery Signature Option, and also FedEx new service (FedEx International Connect Plus).
Please see this video how it works when printing FedEx labels inside Ship&co.
*Ship&co doesn't help you show FedEx rate when checking out, but help you check the actual FedEx shipping fee based on your contract with FedEx when printing FedEx label for your Shopify order.
To show the FedEx rate when checking out, you can manually set it (Settings >> Shipping and Delivery >> Manage rates >> Create shipping zones) or use this free feature from Shopify (see this link).
Please let me know if you have any questions!