But any of the ryokans discussed here will certainly have Western style toilets (well, actually Japanese TOTO washlets, haha)

Also, for the OP, I would probably go to Gora Kadan if you're planning to go to Hakone. I think it's really fantastic and the food incredible. I personally tend to find you can "get more out of the experience" if not doing a ryokan in Kyoto. Note though that Gora Kadan is not exactly traditional: the place is a fairly recent build and feels modern (although the service is very traditional).

However, if you'd rather be in Kyoto, the places listed above are excellent, traditional ryokans.