Grazing is not really recommended in Japan. Walking while eating can be seen as impolite. But one place where there are lots of small bites for sale is Tsukiji Market. If you do want to graze here my only suggestion is that you step off to the side and eat before you move on. Tsukiji has become so crowded that it is safer to stand off to the side and finish eating. Here are a few places to get a quick bite:
There are a few tamagoyaki (Japanese omelet) shops at Tsukiji Market but this is the only one that I am aware of that sells it on kushi (skewers). There are four flavors: plain, anago (eel), kani (crab), and ebi (shrimp). If you want to try all four ask for the “aji kurabe setto“.
Yamacho 山長
Chuo-ku, Tsukiji 4-16-2
Tsukiji Yakinosuke also sells food on skewers – grilled seafood. A variety like hotate (scallops), iidako (octopus), or unagi (eel). Beer is also sold here if you are thirsty.
Tsukiji Yakinosuke 築地焼之介
Chuo-ku, Tsukiji 4-8-7
http://www.tsukiji.or.jp/modules/shoplist/shop_detail.php?shop_id=591
I have a hard time walking by the large Kibun corner booth without buying some of these deep-fried squid legs (ikageso age). Kibun is famous for the variety of Satsuma-age (deep-fried fish cakes). I usually pick up a pack to make oden at home, and a bag of the squid to graze on right there.
Kibun 紀文
Chuo-ku, Tsukiji 4-13-18
Food Sake Tokyo 