I know that many people prefer to hose their mowers down with a garden hose. I admit I have done it. Still doing that is risky. If water gets into the wiring air filter or engine you could really do some damage. Hand washing with damp rag is a drag but also your safest bet.
For the past three years we have used the Greenworks 22502 Corded Lawn Mower on our ¼-acre lawn. We particularly like how easy it is to adjust the blade height and it is surprisingly light. There are just a couple negatives we have noticed. We live in the Pacific Northwest where mowing wet grass is unavoidable. When the grass is wet it does not feed into the bag of this mower easily. Also we had to replace the cord after my teenager ran over it with the mower. So cord control is important and takes a little planning.
Place a drip pan or other container on the side of the mower with the filler. Carefully tilt the mower so oil drains out and into the pan. Discard the spent oil into a proper disposal vessel. Now slowly pour fresh oil into the mower. For the specific type of oil you need check your instruction manual. Make sure to add only as much as your particular model requires. Remember to let the mower sit undisturbed for a few minutes so the oil settles properly inside the engine.