你的问题查词典就能解决。《韦氏高阶词典》hesitate

1 不及物：（因为紧张或不确定是否该做某事而）迟疑、犹豫。可后接about/over + doing表示某事。

[no object] : to stop briefly before you do something especially because you are nervous or unsure about what to do

• She hesitated and waited for her friend to say something.

• He hesitated about/over accepting the job.

2 及物（后接不定式作宾语）：（因为怀疑或不确定而）不愿意做某事。

[+ object] : to be unwilling to do something because of doubt or uncertainty

• I sometimes hesitate to say what I am really thinking.

• I hesitated to come without being asked.

• I wouldn't hesitate to ask for your help if I felt I needed it.

• Don't hesitate to call if there is a problem.

        hesitate about  对 ...... 犹豫 : I didn't hesitate about working with Craig. 和克雷格一起工作，我没有顾虑。（摘自《牛津英语搭配词典》英汉双解版）

        She's still hesitating about sending her son to college.  她对于要不要送儿子进大学一事仍然犹豫不决。/ We seldom hesitate about where to stay in Paris. 去巴黎要住哪儿，我们很少有拿不定主意的情况。（摘自外研社建宏《英汉多功能词典》1997年1月第1版）

       [hesitate + to do] 迟疑于做 ... / Don't hesitate to tell me if you have any requests.  如果你有什么要求，请告诉我，不要犹豫。（摘自外研社建宏《英汉多功能词典》1997年1月第1版）

       我没有找到 hesitate to sth 和 hesitate doing 用法的例句。

hesitate  与  do

明显是还“没做”的情况下，才存在“犹豫”，

已经“在做”或“做了”，逻辑上自然就不存在“犹豫”了

所以，自然是 hesitate to do

( 还有一种思考的方法，就是明显不能说“犹豫某事 hesitate sth”

没有这种说法的，一般都不能接doing )

接介词

hesitate  (at/about/over sth)   （牛津高级）

补充几个：

hesitate before doing

hesitate between doing A and doing B

hesitate over whether to do A or (to) do B