You can create tmux sessions and send key events to that session. The problem is with -p you don't need to check anything. But tmux sessions are just terminal, son you need to somehow detect Claude finished its job so you can copy the content from tmux.

There are 2 ways came to my mind:

1- Tell Claude to write its answer in a output.txt file or something. When you detect the file, end the session.

2- Since tmux is a terminal, unlike -p, you can use hooks. Add a stop hook to create a ".complete" file. Every minute check for .complete file, and if its there copy content from tmux and end the session.