Discover client used for remote SSH sessions?

Morning all,

I am trying to simplify user experience for users that connect to our SSH servers. Presently, if they're connecting from certain SSH clients they run one script to set up tmux and keybindings that match that platform. If they're connecting from mobile or web, they run a separate script.

Is there anything I can do on the SSH server side to determine the client they're connecting with? Usually there's four clients: GateOne HTML5 ssh, xterm, putty, or JuiceSSH.