"hesitancy to" is correct and usable in written English.
You can use it when you want to express someone's reluctance to do something. For example, "He displayed a noticeable hesitancy to answer the question."
Why the hesitancy to talk about the steep price of cancer treatment?
Prince Charles's hesitancy to enter the clearing made it clear that he suspected something was up.
In a conference with me, he expressed his hesitancy to even grade the paper.
In an interview, Mr. Ocampo expressed some initial hesitancy to enter the race, given the odds.
He said that played a role in his hesitancy to run.
Jim Baron acknowledges a hesitancy to call too many plays for his son.
But I feel the same hesitancy to claim any of those identities".
Retail analysts say the hesitancy to accumulate more things is increasingly common.
In this country there is a lot more hesitancy to give out the number".
There's a hesitancy to buy in because you don't want to go too far and then have your heart broken".
Their hesitancy to involve themselves in such disputes made the justices' decision to hear the Bush appeal surprising.
