I want to set up my company's server as a gateway to all of our client's servers. So that people I work with can simply 'proxy on through' without needing to set up SSH keys on their machine. I.e.
[My local box] -> [Our Company Server (with SSH keys)] -> [Client's server]
So far I have this in my .ssh/config
Host client-server
User myclient
ProxyCommand ssh -o Compression=no gateway netcat -w 3 %h %p
Compression yes
host gateway
HostName company-server
User me
Compression yes
However this still asks for a password for myclient@client-server. I want it to use the ssh key on gateway. Is there any way to achieve this?