Can we say: He replied rather drily to the question I asked.
"Drily" (or dryly) is an uncommon word. I had to look it up to see if it even existed as an adverb.
As someone educated in the 1950s, I still use "May I...?" when most native speakers use "Can I ...?" for "Have I your permission to ...?" / "Is it OK if I ...?".
In modern English, as most grammarians now agree, "Can I ...?" can mean "Have I your permission to ...?" / "Is it OK if I ...?". It can also mean "Is it possible to ...?"
Even when I was at school, the old:
Pupil: Please, sir. Can I go to the toilet?
Teacher: yes, you can, but you may not.
was regarded as outdatedly prescriptive.