Hi Kay,
The feature you want is on the roadmap of tmate (when I'm done with my phd, I will persue a startup around tmate).
If you want your users to do the recording on their end, my recommended solution is to use the builtin script/scriptreplay commands (which is good, there's nothing to install):
* record: `script --timing=recording.timing.log recording.log -c "ssh
x...@ny.tmate.io"`
* replay: scriptreplay -t recording.timing.log -s recording.log
You can also do some recording on your end, and provide the replay files.
Hope that helps,
Nico.