As requested, moved to answer:

Unfortunately, I think not. The code that tells whether the app will appear in that list is in the app itself: Documentation

However, you state that you are rooted, so what about using Titanium Backup to "freeze" Opera?

Unfortunately, I think not. The code that tells whether the app will appear in that list is in the app itself: Documentation.

However, you state that you are rooted, so maybe you could use Titanium Backup (Pro) to "freeze" Opera.