Option 1 is grammatical and understandable, but it does not sound like a natural, idiomatic Dutch saying. A native speaker would not likely say "Het mooiste geluk is blij zijn" in everyday speech or as a tattoo motto. Option 2 works better as a tattoo because it is a deliberate word list: three separate words, not a sentence. Mixing a noun and adjectives is acceptable in that format, though it reads more like a poetic list than a grammatical phrase.
Why option 1 feels slightly off: Dutch does use "Het mooiste ... is ..." constructions, but they usually sound more natural with a noun or a clear contrast, for example "Het mooiste geluk is eenvoudig" or "Het grootste geluk is tevreden zijn." "Blij zijn" is fine as an infinitive, but pairing "geluk" with "blij zijn" creates a slightly abstract, translated feel. It sounds like an English idea rendered word for word. It is not wrong, but it is not the kind of line a Dutch speaker would spontaneously use.
If you want a more natural sentence, consider these directions. "Geluk is blij zijn" is simpler and closer to a proverb. "Het mooiste geluk is tevredenheid" is more idiomatic but changes your meaning. "Blij zijn is geluk" is short, natural, and puts the emphasis on joy as the definition of happiness. If you want to keep all three ideas, a list is often the safest choice for a tattoo.
For option 2, "Geluk · Mooi · Blij" is visually clean and avoids grammar problems. The mix of noun and adjectives is not a mistake in a tattoo context. Dutch tattoos often use single words or short lists without articles. Just be aware that "mooi" means beautiful or nice, not exactly "wonderful" in the sense of amazing. "Wonderful" could be "wonderbaarlijk" or "prachtig," but those are longer and less common in tattoos. "Blij" is the everyday word for happy or glad, while "vrolijk" means cheerful. If your nickname means joy, "blij" is close, but "vreugde" is the noun for joy and might match better in a list.
A few practical next steps. First, decide whether you want a sentence or a list. Sentences carry more risk of sounding translated; lists are more forgiving. Second, ask a native Dutch speaker to read your final choice aloud and tell you if it sounds like something they would say. Third, consider a short, well-known Dutch proverb if you want maximum naturalness, but only if it still matches your personal meaning. Finally, have a Dutch-speaking tattoo artist or a native speaker check spelling and punctuation, especially the middle dot in option 2. If you want structured help evaluating phrasing, a resource like Dutch Fluency can explain natural collocations, but for a tattoo, a quick native opinion is best.