There is a Japanese site http://www.usskyushu.com/trekfont.html which has a home-brewed katakana Star Trek font.
It is very limited (only contains katakana), but it does work. In that font your picture looks like this
(The font doesn't contain numbers nor kanji or hiragana, so I had to write all of it with the available glyphs in katakana.)
The site said that even though there are many Latin Star Trek fonts out there, there aren't any for Japanese (except for the one apparently used in the movies). That's why he tried to reproduce it himself. (Maybe this means that there is not a more complete font out there...)