Solving the problem of having a personal and a work GitHub account is really trivial without any extra tools. All you need is a dedicated SSH key for that GitHub account. (And why would you have a password for a ssh key on your personal machine?)
~/.ssh/config
Host github.com-work
HostName github.com
User git
IdentityFile ~/.ssh/work_id_rsa
IdentitiesOnly yes
~/.ssh/config
~/.git/config