As a foreigner with a Japanese name, what are the implications of writing my name in katakana or kanji?

I'm a foreigner, and my name is Shiori. I've heard of a several Japanese people with this name, and they write it with kanji (of course).

I know that when you are a foreigner, you are supposed to write your name in katakana, but since my name is Japanese, is it possible for me to use kanji?

According to wikipedia; the most common ways of writing Shiori are 栞, 撓 and 詩織. I know that foreigners should avoid kanji for their name because even if it sounds like your name, the meaning comes out as weird. But these kanjis for Shiori are already used for names, so the meanings don't come out as weird..?

So even if my name is Japanese, should I use シオリ or any of the kanjis?