The sentence can also be interpreted as "you seem to have free time koga-san" in a jumbled kind of way. 手すき means "to not be busy", but can also be read as "hand love".
So I think Aya wanted to say that Mitsuki seemed have a lot of free time if she was trying out a new pick instead of studying and fumbled it in her half-asleep state. And Mitsuki read it as "I might love your hands".
oh cool, thanks for the addition (and the great translation as always). I thought it made sense since she's sleepy and all, like that lyric I quoted that's drunkenly stumbling through words.