Will your router accept a public/private key pair for authentication instead of using password based auth?
A few years ago, I was controling a netapp storage device from perl, and I found that it would maintain a list of authorised public ssh keys. Once I had added my public key to it's keyring, I could then have my perl script connect using a private key, and without the need to handle password prompts. The connection went directly to a shell where typicaly my script would issue one command, capture the output and then dissconnect. This made that part of the script much simpler.
One issue to be aware of, is that the device I was connecting to did not like it if there was an SSH agent which offered several different keys until one was accepted. If the first key offered was not acceptable the connection got dropped, there was no possibility to try a different key or drop back to password based authentication, so when you test, you should add -a to your ssh command line.