Totally safe to have uncovered
Bacteria can't jump off the fish and fly through the air. They can't crawl, swim, walk or ride bikes between items in the fridge by themselves. If you carefully place it in a clean container it is safe. The aroma may carry, but if the fish is fresh it should have little aroma and this will dissipate anyway.
Better Yet, dry it on the counter at room temp
You can also just have the fish out on the counter. This will bring it closer to room temp, and much of cooking and creating good texture is about temperature differences. Starting the fish at a warmer temperature will also help to create good texture and not stick. Do not worry about the safety of this. If the fish is fresh, any bacteria growth that might begin will be immediately killed in the cooking process. You can blot the fish gently right before cooking with paper towels for maximum drying. If the fish is still cold it will have condensation continually forming.
USDA guidelines show the time that food can be in the danger zone. Don't be alarmed by the 'doubling every 20 minutes.' Everything we touch, eat, see, taste, smell has bacteria on it or in it. It takes many doublings and the bacteria have to emit the toxins for something to become dangerous. If you hold food at room temp, it is coming out of refrigeration and into the danger zone, then will be cooked, ending the cycle. If the fish is poor quality to start with AND you have immune system deficiencies, then extra caution is required. Aged, infirm, or otherwise compromised immune systems should be treated with more caution.