"happy nonetheless" is correct and usable in written English.
You can use it to describe someone who is content or pleased despite the surrounding circumstances. For example: "The family had to cancel their vacation plans due to the pandemic, but they remained happy nonetheless."
He is happy, nonetheless, to be able to enjoy the hills as he used to.
The selection wasn't as robust as a summer market, but shoppers seemed happy nonetheless.
I'm very undeserving to be here, but very, very happy nonetheless.
He did not get the opportunity but he left happy nonetheless as Anthony scored 28 points to lead the Knicks to an 89-86 victory.
I had gone for a pizza, only to learn that the wood-burning oven is not fired up at lunch; I left happy nonetheless, though I still haven't tried the pizza.
Matt Asiata has managed just 36 yards from his 20 carries so far today, but anyone who picked him up as a Fantasy fill-in for Peterson can be happy nonetheless after the running back takes in his second touchdown of the day, powering across the line from one yard out after Cassel set things up with another big completion downfield to Chase Ford.
Gooch is happy to acknowledge nonetheless an outstanding individual performance from Australia's resurgent left-arm fast bowler.
She ponders this for a while, perhaps having anticipated this line of retrospective inquiry, but not that happy with it nonetheless.
The Barbury Castle trainer admitted that Katchit would have been better suited by Cheltenham, where he has won on five of his six starts, but is nonetheless happy the International has been saved.
While refusing to commit Britain to the 2% target for defence spending, the government was nonetheless happy last month to confirm that, regardless of circumstances, DfID would receive each year 0.7% of GDP.
The compilation film "Six in Paris Parisris Vu Par... .....), from 1965, screening at BAM Oct. 3-9, is a not terribly distinguished but nonetheless happy souvenir of the New Wave, when films could be thrown together casually.
