Is it easy to find rain overshoes or protection for shoes in Japan?

I leave for Japan (Osaka and Kyoto) in about two weeks, and I'm really excited...but nervous about my shoes. I've always had hot feet and can't walk around comfortably in closed shoes, so my two pairs of walking shoes look like Mary Janes (with orthopedic soles). They've served me well on many trips.

But I'm getting worried about the rain. If it rains a lot, I hate wet socks. Do places like konbini sell plastic overshoes or garters for rain, or is this a more obscure thing to find and I should just order some before I leave?