Mouse urine and droppings dry out relatively quickly, but just removing moisture doesn't kill germs. When you come along with your broom and dust mop (or vacuum cleaner), you scoop up most of the mess, but microscopic bits are released into the air where they can be inhaled and spread disease. Very bad idea. Instead, the U.S. Centers for Disease Control and Prevention (CDC) recommends saturating rat droppings, rat nests and any areas where rats have lingered with a disinfectant mixture that kills germs on contact.
Although you can use an over-the-counter disinfectant to do the job (make sure it says disinfectant on the label), the CDC also recommends using a mixture of one-and-a-half cups of bleach to a gallon of water (a 1 to 9 ratio). Spray affected areas well, and leave the bleach or disinfectant in place for 5 to 10 minutes.