LEDs are counter productive to sleep. The solution here would be a safe candleholder that is able to be left unattended without setting fires.
There are a lot of anecdotal stories out there where people get a reduced sleep quality after switching to LED lighting in the bedroom. Is there something deeper to the story? Quite likely. The question now would be whether this affects everyone or if those people are outliers.
But I'm thinking of the tea light replacements that are sold for use in jack-o-lanterns. They intentionally "flicker" in a candle-like way, instead of the kind of flicker you describe.
LED devices can also produce a wide range of color temperatures (esp when filtered and diffused), so there's no inherent blue light problem.