I've not been yet, but the Tokyo Sanuki Club near Azabu Juban station has (in their words) "been chosen as Sanuki Embassy for the successful appeal of Kagawa"
What I guess this means is that the Sanuki Udon here is approved by Kagawa and one of the club's functions is to promote the Kagawa region in Shikoku.
http://www.sanuki-club.com/English/top_english.htm
The place has a restaurant, garden, and a range of accommodation options (all reasonable) including Japanese tatami rooms.
It should be quite simple to ask for your udon to order here, selecting a range of toppings that do not include fish.
(I'll ammend this post with a first hand report in a few weeks time)