I don't wear goggles. I use an old shaving brush and lather up a mug of shaving soap. I hose down my helmet then brush along the cushion pads and straps of the helmet. I then hose down to rinse and leave on the back porch to dry. I wash my bicycling gloves after I do the dishes and hang them over the sink to dry.
A shaving brush can be had for cheap at any pharmacy and won't scratch up a nice helmet.
Ernest
PS: Some people here just take the helmet with them when they shower and both get clean at the same time.