The way that it works is that your hosting provider will have a number of ciphers installed and available. When you connect to a remote server like authorize.net it will list supported ciphers and the server will use one of the supported ones provided it is installed. Authorize.net is going to stop including RC4 in the list of supported ciphers and your server will automatically just use another one that is supported.
This is nothing for you to worry about. Everything will continue to work after the transition without the need to update any code.