One way to do it is to edit /usr/share/byobu/keybindings/f-keys.tmux
.
You will find these lines :
bind-key -n M-Left previous-window
bind-key -n M-Right next-window
M
is for Meta, aka the ALT key. Change the lines for :
bind-key -n C-S-Left previous-window
bind-key -n C-S-Right next-window
C
for Ctrl key and S
for Shift key.
Save, quit, press F5 to reload profile.
Refs : Bybobu doc, Byobu-and-mc, keybindings-in-byobu-using-tmux-backend, tmux