Though the actual risk is very small, it is not a good idea to make it a habit to touch blood, or blood stained material including dressings or paper with your bare hands, especially if the blood is still liquid and fresh. Most disinfectants kill disease agents and are sufficient to wipe on your hands, however some agents are better than others. A very dilute household bleach is very good as far as HIV is concerned.
Using the same sink for dumping residual urine samples and for taking water for coffee etc is safe, but not very aesthetic! After all one takes water from the faucet and not from the basin of the sink.