"without wavering" is a correct and usable phrase in written English.
You can use this phrase to indicate someone's perseverance in the face of obstacles or opposition. For example: Despite her difficulties, she kept pushing forward without wavering.
Whatever steps need to be taken we will take them without wavering".
To close out the first set, she pounded an overhead without wavering.
Approaching the first test, she wore two-inch heels and strode purposefully back and forth, without wavering.
As an early leader in the campaign, with a target on her back, she has faced anger and derision without wavering.
Without wavering from his campaign's insistence that he has a "path to victory", the senator from Vermont said his goal was to increase voter participation in politics.
We'll also have the chance to ask him about the larger implications of facial recognition and what it means to build a business without wavering on your principles.
Try holding a scream for as long as possible without it wavering.
Armstrong's voice soars and floats without breaking or wavering for a second, as if he has been instructed by the very best vocal coaches for years now.
"We have spent 40 years dedicated to building KISS without quitting or wavering as the band has moved forward with huge tours and platinum albums through different important lineups for 40 years, to this day.
Ailred of Rievaulx wrote in David's eulogy that when David came to power, "he found three or four bishops in the whole Scottish kingdom [north of the Forth], and the others wavering without a pastor to the loss of both morals and property; when he died, he left nine, both of ancient bishoprics which he himself restored, and new ones which he erected".
Nothing would change in either direction without the support of these uncommitted and wavering citizens.
