'asked cautiously' is a correct and usable phrase in written English
You can use it to describe when someone is speaking in a hesitant or unsure way. For example, "He asked his boss for a raise cautiously."
"So, could you outrun a T. rex?" L. asked cautiously.
The young lady asked cautiously how it was "all antee".
"So, what are the superheros going to wear?" I asked cautiously.
"So, what do you think about that?" he asked cautiously, wanting to get her opinion on the whole Daniel thing.
Not to be intrusive, but do you mind if I ask you a few questions?" "Like what?" I asked cautiously.
Her friends, knowing she wanted an escape from soccer, nonetheless asked cautiously, "Is it O.K. if we talk about the World Cup?" and Sundhage smiled weakly and said it was.
Likewise when 29-year-old Karina from Essex tries to explain her job ("What's the correct term?" a producer asks cautiously. "Stripper?" she laughs) to 30-year-old Londoner Michael, who is still reeling from the end of a long-term relationship.
If you do not know, consult with your accountant, and also ask, though ask cautiously (trust your gut) your Leasing Guru's suggestions are.
"What do you think of the term Asperger's syndrome?" I ask cautiously--for yes, this is his label, a neurobiological condition at the high-functioning end of the autism spectrum.
They asked questions cautiously: Did I live near New York?
I caught a glimpse of that when she asked me, cautiously, "Wouldn't you say that anybody who thought as much about balance as I do in my work probably felt some threat to their balance?" After a long pause, she added, "Of course all adolescents are out of balance, and very aware of it.
