Have you tried vimium? It's amazing. You can press a single key to search tabs, a single key to search history, bookmarks, and many other functionalities. Not using a mouse is also pretty easy with the link navigation feature (f by default), but even with one hand the commands are so succinct that it works well.
This is one of the things I love about my Emacs config. I just hit a key to get things like buffers or file trees up when I need them, then they disappear.
I'd love to have a keyboard driven browser but whenever I've tried I always end up with one hand on the mouse anyway so it doesn't work.