DIAGNOSIS You're right to be cautious. The interior is plastic and the door seal is vinyl. Harsh chemicals or abrasives can crack plastic, stain it, or degrade the door gasket, causing leaks.
FIX Here's the shop-teacher approved method. 1) Unplug the fridge and remove all food and shelves/drawers. Wash the shelves in warm soapy water at the sink. 2) For the interior liner, make a cleaning solution of 2 tablespoons baking soda dissolved in 1 quart of warm water. 3) Use a soft cloth or sponge dipped in this solution to wipe down all surfaces. The baking soda is a gentle abrasive and deodorizer. For sticky spots, let the solution sit on the spot for a minute before wiping. 4) Rinse with a cloth dampened with clean water. 5) Dry thoroughly with a towel before plugging back in.
IF THAT DIDN'T WORK For really tough stains or mildew (common on door seals), use a 50/50 solution of white vinegar and water. Vinegar disinfects and cuts grime without damaging the materials. Test it on a small, hidden area of the gasket first.
HEADS UP Never, ever use cleaning products containing chlorine bleach, ammonia, or abrasive powders like Comet. They can permanently damage the plastic and create cracks where bacteria hide. Also, never pour water directly into the unit or use a spray bottle that could let liquid drip into ventilation slots.