Asking if you *should* play cash games, MTT's, or S&G's is like asking what your major in college should be.
The answer is: Do what you enjoy.
If you feel that you want to expand your game into various formats (S&G's, or 6-max, or MTT's, or whatever), or different games (Omaha, Razz, 8 Game, etc.), well then do it.
Professional poker players need to be well rounded, because the want to hit the games that currently have the highest rate of return. Some days there will be juicy No Limit Hold'Em tables, other days the NLHE tables will be dry but the Omaha games are juicy.
But you're not a professional. You have the luxury of playing for fun, so follow your heart.
When I started playing I assumed that I'd only play tournaments. But then I started experimenting with ring games and found that I enjoyed the decreased variance. That is, I liked that I could buy in for $5 and leave most games with a small profit. I liked that better than losing S&G after S&G to hit the occasional big profit. (I learned this with play money so when I deposited I was almost exclusively a ring game player)
You mentioned that you have some hesitation about your short handed and HU play. This is *exactly* why you should play S&G's rather than MTT's.
The real money
at the end of any tournament is in 1st place. The difference between 1st and 4th is often huge.
It would suck to get to the end of a 6 hour MTT and you miss out on hundreds or thousands of dollars because your endgame wasn't what it could be, because you lacked experience.
So I recommend practicing in cheap S&G's. The kamikaze nature of engame play is quite different than cash game play. I know I had trouble adapting, and it took Harrington on Hold'em Volume II to finally get me to step out of my nitty ring game comfort zone to do what is necessary to win tournaments.