It´s not about wrong vs right.
To #1 you are stating that it won´t be a good experience to see you singing, perhaps you are warning someone else that you have a bad voice.
The focus is on the activity, (my singing - problably you are talking about your hability of singing well or singing skills"
Sentence #2, in practice (and translated into Portuguese) would be the same as #1, but then the focus is more general in kind, you singing some song, but then in a general way. Sometimes meaning that is because you don´t sing well, your voice is bad, etc. But your focus isn´t on the skill per se.
To # 3, one would expect some more elaborating, that is, something to complement the information, sing what for example, or then you would have talked about the song beforehand.
One example from the Web: "to see me sing the whole song, please go here" (next, comes the URL to click but at this point you know what the song is about, the guy have let you know). Also notice that after the verb "sing" it explains what is about (the whole song).
"you don´t want to see me sing." to me, leaves something pending, we would expect the something more to complete the "sing" part.