The phrase 'without worry of' is correct and can be used in written English
You could use it in a sentence to describe something that is done without any need to worry about an unfavorable outcome. For example, "He went into the exam without worry of failure."
They happily leaked classified information to journalists – much of it false – without worry of consequence.
A surfer walked across the street in evening's slanted light, carrying his longboard, without worry of traffic.
To have money and food, and live without worry of being tortured, or having their homes forcefully demolished.
The change, he said, would allow "citizen journalists" like bloggers and collaborative Web sites to link to the material without worry of copyright infringement.
Led by Senate Minority Leader Mitch McConnell, they constructed a First-Amendment theory to fit this benefit, saying that secrecy protects free speech (for corporations) without worry of harassment.
I can let myself heal without worry of time.
Same-day voter registration, as we have in Minnesota, enables citizens to vote without worries of missed registration deadlines.
Now it plans to advertise the fact, in many languages, that illegal immigrants will have safe access to services in the city without worries of being reported.
There is no longer any excuse for anyone to be depressed or unhappy; even "normally" happy people can make themselves happier without worries of addiction, hangovers, or long-term brain damage.
In the long term, we're still focused on becoming the place for people to post forever — a stable platform that will operate without worries of the site, team, or mission disappearing.
Although we would rather live without the worry of allergies, good things have come out of it.
