As a right-handed person whose first language is English, I have a natural rightwards slant to my handwriting much of the time, depending on how quickly I'm writing and what physical position I'm in as I write.
I've noticed I sometimes impart this slant to my Japanese writing as well, when I'm practicing writing out sentences.
Is this as normal in Japanese as it is in languages that use the Latin alphabet? Will rightwards-slanting kanji/kana seem odd? I haven't been involved with Japanese long enough yet to even learn whether there's such a thing as italics in Japanese, so I'm not sure how it would be perceived.