'not without trepidation' is correct and usable in written English.
You can use it in situations when you are feeling nervous or apprehensive about doing something, or when you are aware of potential risks or dangers. Example sentence: I sent my weekly report in to my boss, not without trepidation.
But the selection of Mr. Ali was not without trepidation from some members of the group.
A friend suggested going on a mission, an idea Coleman embraced but not without trepidation.
And while the company had willingly taken the risk that it could end up winning, it was not without trepidation.
He says that fond memories of that story, which was written by Bryan Di Salvatore, persuaded him to coöperate for this story, although not without trepidation.
"I think we need a new name for it," she wrote, and in the past decade we have mainly settled on "reality television," although not without trepidation.
This time it is the Belgian royal family, gingerly following in the footsteps of their British cousins, who have announced - not without trepidation but with some relief - that Prince Philippe has found a bride at last.
We made plans to go to New York City on that Saturday, but it wasn't without trepidation that I agreed.
Ms. Morrow, who has been the director for five years, also conceded that the original decision to include both groups was not made without trepidation.
In keeping with my New Year's resolution to take better care of myself, it was not without some trepidation that I drove to my internist's office in Livingston for a physical.
So, like I said, when I caught word that there was to be a sequel, it was not without significant trepidation that my eyebrows were raised.
When God described the Yom Kippur service and ordered Aaron into the Holy of Holies, he went--though, I imagine, not without some trepidation.
