I'm an emacs user, not vim, but I have some idea. My tmux.conf reads like this:

  unbind C-b
  set -g prefix `
  bind-key ` send-prefix

This removes Ctrl-b as the tmux prefix, sets it to ` (backquote) instead, and makes pressing ` twice insert an actual `.

It really doesn't take very long to get used to typing `` when you mean `.