Thinking of i18n as an afterthought is always a nightmare :)
Well, the short answer is "yes, you can", but you need a very good reason to do so. Almost all modern games use both hiragana/katakana and kanji, unless the game is clearly targeted at kindergartners.
- In general, ordinary Japanese sentences can express the same thing in much smaller number of characters, thanks to kanji. That means, for example, if you have a text box that can contain 4 lines of strings in English, there is a good chance that you can turn it into a 3-line box and show the same message in Japanese with a bit larger font.
- Native Japanese speakers are able to read Japanese sentences with surprisingly small characters, as long as you choose the right bitmap font. 12–13 pixels per character is usually sufficient (see examples in this page), but I believe most modern LCD can afford much more pixels per character.
- There are a few modern games which intentionally chose non-kanji UIs for stylistic reasons. For example, the Japanese version of Terraria uses very few kanji even in the PS4 version, and all of the item names are in hiragana and katakana. But this is obviously because they wanted that "8-bit" look and feel in their game. Unless you need this effect, you should try to use kanji.
I recommend that you show your game to native Japanese speakers (hopefully gamers) and seek for their advice. Giving up kanji altogether is usually the last thing to do.