This is not possible by design while using Citrix Director for shadowing ICA session on 7.x. However, as a workaround you may try to use session recording server which has the option to start recording the user session without any prompt shown.
There is an integration with Director which lets you start recording with a single click:
https://docs.citrix.com/en-us/xenapp-and-xendesktop/7-6/xad-monitor-article/xad-session-recording.html
By Design.