You should be fine. You have the washer on one end, directly over the legs. The washer doesn't weigh anything close to that and there are no dynamics here. Avoid earthquakes. Just give it a test. Fill your washer and see what you think.

You can get little plastic stools for sitting in showers. They look really flimsy, but support people all the time. One would certainly support your washer. Or put it on the biffy and gain some counter space.