My Chinese name in Kanji is 王元劭 (Wang Yuan Shao). I've heard there are many different readings I can use for each kanji, am I allowed to use whichever reading I like? Also, apparently the character 劭 is a hyogai Kanji, which means I can't use it.
We are supposed to call your name おう・げんしょう unless you challenge it. If you want to be called differently, go ahead and offer it. In that case, you'd use katakana like ワン・ユァンシャオ.
p.s. I'm Japanese but I haven't heard that one cannot use hyogai kanji.
The way I usually see foreign names written in Newspapers etc is that Kanjis that are not hyougai are used, with the original pronunciation transliterated as furigana, and instead of the hyougai kanji, katakana is used. An example is the Go player 李世乭, where 乭 isn't used in Japanese. The way his name is usually written is thus 李｛イ｝世｛セ｝ドル