Do I need to apply for a business visa or tourist visa?

Hi, I am Brazilian but I leave in Denmark.
End of this month I will have 2 days meeting in Hong Kong and then, possibly 2 days for tourism in China.
Do I need to apply for business our tourist visa?
Does the same visa is going to work for China and Hong Kong or I need to get separately?
Final question: because I wil be travelling most of my time this month it is difficult for me to leave my passport at the embassys for many days, even 3 days sometimes is quite challenging. So, may I ask what is the minimum time I can expect to get my visa and passport back?
Many thanks in advance, Jose