Speed training could up your speed in the Stamina and Strategy training.
Accuracy could help your balance for the Willpower training, or perhaps slightly increase the range of your reach for Strategy training.
Strength could help with the Stamina training, or let you swim harder in Speed training.
Strategy could improve your control in the Willpower training or let you hit the dummies in the Accuracy training better.
Willpower could decrease click time/difficulty for the Speed and Stamina training.
I think this would be a neat way to tie all the skills together. It would offset the difficulty curve a bit, but it would encourage you to travel and level up all of your skills evenly.
(Or maybe some of these do have an effect in addition to the Stamina/oxygen connection, but I haven't noticed it because the leveling up is gradual.)