You cannot. tmux only allows single-key bindings (either alone, using bind-key -n , or following the prefix key).

However, you might try binding "v" to an invocation of command-prompt :

bind-key v command-prompt "tmux-vim.bash %%"

where tmux-vim.bash looks something like

if [ $1 = "G" ]; then tmux split-window "vim +$" fi