User agent is a HTTP header, and SSH doesn't use the HTTP protocol. Therefore, SSH cannot specify a user agent.
It's more likely that destination port 22 is blocked. To circumvent this, you can specify additional listening ports on the server in
# What ports, IPs and protocols we listen for
In your client machine, you have to specify the port either manually when connecting or in the config file.
Example for manual method:
ssh -p 8080 example.com
Example entry in system-wide
/etc/ssh/ssh_config or the per-user
If your conections get blocked due to packet inspection, you may need to use a HTTPS proxy. Apache2 can be used as a proxy if it's already installed.
If you install a HTTPS proxy on your server, you can use this command
ssh -o "ProxyCommand nc -X connect -x example.com:8080 %h %p" example.com
Port ProxyCommand nc -X connect -x example.com:8080 %h %p
in a SSH config file.
You could also use a web-based solution like shellinabox.