For this, I think it's mostly a context thing. If you were going around a circle stating hobbies and you said "puni au i ka hīmeni" it would be interpreted as you like singing, yourself.
But it can also be said in reply to a question about what type of music you like--in this case it would be interpreted as "i like singing types of music" or "i like hymnal songs."
It's kind of the same in english when you think about it: "I like singing" might be interpreted either way depending on the question.
And just as you can clarify in english you could do so in hawaiian as well and maybe say hō‘ike hīmeni or ‘aha hīmeni to specify singing performances or vocal concerts. :)