The expression 'walk happily' is correct and usable in written English.
You could use it when you want to express that someone was walking with joy and contentment. For example, you could say, "After winning first place in the race, he walked happily back to the starting line."
Your name and photograph appear on the register, the cashier gives you a nod, and you walk happily out the door with your artisan shade-grown organic coffee.
Neighbors have joined in, like the one who wrote: "We walk happily/ You honk in snarled traffic/ Who gets there first?
Every woman wants to walk happily ever after in whatever footwear they own.
It is easy to "walk happily ever after," because there are many over-the-counter foot products that one can buy to customize those hot, stylish, evil shoes in your shoe wardrobe and make them more comfortable to wear.
That didn't come with a giddy, Champagne-bathed celebration, just Cabrera walking happily to the dugout while an appreciative Kansas City crowd showered him with appreciation.
We fortunate pilgrims walked happily home, reassured that in matters of the spirit and the table, Rome really is the Eternal City.
The willowy star simply walked happily to the net, offered some sympathetic words to Justine Henin and waved into the long-lens camera that Williams's father had aimed in her direction.
I mean, you and I are walking happily down a little alley in a small town, but really around us all kinds of stuff is in dire trouble — you know, banks in dozens of countries, people in Iceland are hoarding food.
The sun was setting slowly in the distance, and the father walked happily across the lawn to the entrance, to the right of the gate, and took the stairs up to a high floor, to the apartment where his daughter was.
"And she walked happily ever after"®.
