The word ‘dryly’ as an adverb
My Dictionary says:
dryly |ˈdrīlē| (also drily) adverb
1 in a matter-of-fact or ironically humorous way : “How very observant,” he said dryly.
2 in a dry way or condition : Evans swallowed dryly.
I also found it can be a synonym of "being cold" and not just "ironic" and "sarcastic".
Yes, that is correct. 'Dryly' is the adverbial form of the adjective 'dry', and the adverb is called for in this case, since it modifies the verb.