The problem however is that I have very little self confidence in my
own health and strength. I catch colds easily, and can't eat all types
of foods, etc etc.
This is a profound personal observation with regard to your training as a martial artist. Most martial art schools you may train in will naturally address these concerns as a matter of course, by simply engaging in training.
However, if the health and nutrition aspects are of some concern, then may I suggest that you also look into health and nutrition as an adjunct to, or complimentary regime with, your martial arts training.
You WILL get fitter and healthier by training at a decent school - unless of course you have a chronic condition, or medical issue that needs addressing - then your training may in fact become a danger to your health. It's a simple as A - B - C. A= AWARENESS (you are aware of the problem). B= BALANCE ( you are seeking a balanced approach to training - body and spirit). C=CONTROL ( you are wanting to control your confidence and health issues, and thus your destiny).
What kind of martial arts out there focuses not so much on strength,
but rather on building confidence and spiritual peace?
is most obviously the one that allows you to to focus on the latter building confidence and spiritual peace.
The other aspect is focuses not so much on strength Again, the one who's focus is on BUILDING strength.
I answer your question at the end QUILLION because most persons who ask a question have a lot going on in their statements that set up the question. Peace Mad Merlin