ためらわずに

without hesitation

→ ためらう
phrase Rare #41,188
without hesitation Means “without hesitating” or “without hesitation.” Often used to encourage someone to do something freely or promptly. The ~ずに ending is a somewhat formal or literary way to mean “without doing.”
JA: 分からないことがあれば、ためらわずに聞いてください。
EN: If there's anything you don't understand, please don't hesitate to ask.

彼はためらわずに分け前を取った

He took his share without hesitation.

ためらわずにどんな質問でもしてください

Please feel free to ask any questions without hesitation.

私はためらわずに彼の依頼引き受けた

I accepted his request without hesitation.

彼女にプロポーズする好機ためらわずに利用しろよ

Don't hesitate to seize the perfect opportunity to propose to her.