Seems like it’d be better to determine the script used by the characters in the alias, at least if we’re only going to use it to pick a best alias to display. The Unicode data file contains that data for each character.
Or just do it based off language — I’m sure that is a 95% solution. English, French, German, Spanish, etc. are always written in the Latin script. Sure, Japanese uses two scripts, but that just means you only display it to Japanese users (or maybe Chinese users would prefer it, despite the Hiragana). But this seems very much like a case of take the 95% solution, it doesn’t stop you from fixing the remaining 5% later, if ever.