Here is one miso recipe thread:
Miso Soup
and, here is another:
What is the best miso soup (miso shiru)?
If you type "miso recipe" into google you'll get a countless number of recipes for it...
There are three ways you can go, miso paste with bonito etc (dashi) included (just add water), miso paste + dashi soup stock, or last and in order of most complexity, miso paste + home made dashi soup stock...
I suppose you could make your own miso paste, but who has 6 to twelve months....? Come on.
I'm not an expert on udon (nor on miso for that matter, but I've made the first two basic varieties I described), but udon is basically dashi stock & shoyu (a type of soy sauce made of soybeans & wheat)...
Here is an udon thread:
Udon eating thread
I don't know what your experience is with cooking Japanese food... mine is fairly basic, meaning--- I stick to store bought dumplings etc, I don't completely do it myself--- But regardless, it's still quite common to simply buy pre-made miso, squeeze it in a bowl and add hot water in Japan. This is true of many types of Japanese food which you may get just as much enjoyment from.
Tempura is a great addition to udon, but your husband doesn't like fish, and baring vegetables, you're afraid of hot grease.
Miso & udon are pretty common foods, so there should be a wealth of information out there if you just search for it.
Here's one:
http://www.bob-an.com/recipe/dailyjc/basic/udon/udon.html
ps. You do realize that the main ingredient in dashi is
bonito, a type of fish. Maybe if you keep this under your hat your husband will never know--- But to me this flavour seem inherent to miso & udon...