Using a power drill and paddle attachment mechanizes the job of stirring paint, but it can cause splatters. One way to solve the problem is to use a paper plate. Punch a hole in the center of the plate and push the end of the paddle attachment through the hole before chucking it into your drill. Then hold the plate down over the open can while stirring.
For bathrooms, ASHRAE 62.99 recommends that you exhaust 25 cubic feet per minute (cfm) with a continuously operating fan, or 50 cfm with a fan that you turn on and off as needed. Note that you might incorporate a bath fan into your overall ventilation strategy.