Pat,
Try to find the entry point and block it ( them ) up or you will probably will get a repeat of the mouse problem . The respirator, rather than a paper mask is a good idea when cleaning the droppings and above all wear disposable gloves if you handle the trappings . If you are using spring traps , again, use gloves and spray the traps with a solution of javex to kill bacteria or parasites before resetting them. Mice can carry parasites which if they get under the fingernails can cause flu like sickness.
Sticky glue boards baited with a small ball of cotton batten covered with a bit of peanut butter is effective - just garbage the board and the trapping.
Regards,
Jim