I hate icing too (I know, the horror). I just scrape it off. It's ONE reason why I prefer fondant cakes. Because one doesn't eat the fondant but peels it off like an orange. You get the pretty cake, but don't have the icky old frosting to deal with. Marzipan is another option.
Banana Bread
Cream Cheese frosting or none
Cinnamon Roll w/ Raisens (no icing, most of the sweet is the yucky icing)
Egg tart , Moon cakes , other Japanese/Chinese pastries (they're less sweet than american sweets... something of a savory sweet blend. Hard to describe).
Tiramisu (sans the alcohol)
Icecream Cake (make it yourself by half melting the icecream, squashing it into a cake pan, freezing it super super hard on the lowest cold setting, put a thin layer of cake, about 1/2 inch between layers, ice if you like, keep frozen until an hour before eating, and put it in the fridge)
Soft Pretzel (screw sweet since he doesn't like it, it's supposed to be a treat, and if he doesn't like sweet, he doesn't like sweet) The 'cake' is just supposed to be a treat. It doesn't have to be sweet. It can be a muffin, mashed potato or rice sculpture, filet minion (wait, not in Nippon, too pricey)... point is: Something you can stick a candle in.
Mochi (real mochi) with candles in each mochi if he likes them
Red Bean Buns (if he likes those)
Even mikans. Sort of Croque en bouche style. Or heck... croissants croque en bouche. Or even croque en bouche!!!