Hyphenated wellness is the standard form of this noun. The welfare of one word and the welfare of two words are not accepted variants. Remember that it is well an adjective and to be is a verb. To form a noun, they must be hyphenated; welfare is not a compound word.
In much of the English-speaking world, even in the United Kingdom, and especially in Australia, well-being is usually a word, without a script. Although the hyphenated form is older and still acceptable everywhere, the one-word form has existed for several centuries and has become increasingly common over the years. Today it is not questioned outside of North America. And Canada, for its part, the one-word form is still rare, appearing only a small fraction of the time.
In North America, the word is written with hyphens, well-being. The spelling checker does not capture well-being, and that form appears occasionally in edited texts, but its rarity suggests that it still has a long way to go before it gains full acceptance. Unfortunately for you, language doesn't always work for people's aesthetic values. Choosing the spelling of a word based on its appearance does not make sense.
Obviously, not sticking to the original word with the apostrophe in it* stares at you and then wipes with your hand down in your literality*. Those were examples of how I could have rephrased the paragraph I wrote. You can stop jumping on the WonderWoman train now, pal. Congratulations on the replay.
How was the UK? How was the UK? It doesn't make sense to use a hyphen in the word Wellness. The word welfare is a common misspelling of welfare. Noun welfare consists of an adjective and a verb, so a hyphen is needed for words to become one. Well-being as a word without hyphens is the standard spelling in the United Kingdom, Australia and other English-speaking countries outside North America.