Is this usage of 'curiously' correct?

I recently used a sentence similar to the following:

Curiously, do you prefer black?

Some people found it grammatically incorrect. That was a surprise, for I thought it was perfectly okay. Someone even came with an alternative:

Out of curiosity, do you prefer black?

Is the second sentence actually better? Is there a real difference (bar the number of characters)?

Solution 1:

Synonyms for curiously include strangely or unusually. As you can see if you try to substitute either of those into your first sentence, this is not the meaning you're after, and the result is somewhat nonsensical:

*Strangely, do you prefer black?

The second version actually means what you want it to mean, and is the only correct option of the two. Another way to say it would be:

I'm curious: do you prefer black?