Hummm, yes it's a problem trying to write these out phonetically. You'd only say them as written if you were acting comical or over-dramatic.
Try saying "tee-hee" as a whisper, with fast and short syllables. Sorry to put in the vowels when they're not sounded, but if we wrote "t-h-h-h-h" we'd think it was a snake with a lisp. If you want to sound it, use the short "i" sound.
"Tut-tut" (or "tsk tsk") is a click sound starting with your tongue in the "t/d" position. The air is popped backwards. Like a click consonant (the "c" in Xhosa).