Well, first thing to check on your Sekine is if it has eyelets on both the fork and rear dropouts. Then, look at the clearance between the tires and the frame, and between the tires and the brakes. Also, look at how the clearance changes when you operate the brakes. A fender has to fit without being crushed by the brakes...
Fender width is more important than fender radius, but both have to be pretty close to work. Assuming your tires are 27x1-1/8" (28-630 - 28mm tire width, 630 mm B.S.D.) you'll need a fender 35mm wide or so.
I would suggest brand new fenders, racks and handlebars. I really like the Planet Bike Cascadia (35mm road version for you) especially since the local MEC has all sizes in stock for $26 a pair. I really like the Bor Yueh triple branch rear rack, $15 locally, which I bet is more solid than the old rack on that cruiser. As for handlebars, look up the Wald 8095 or other handlebars in the Wald lineup. If Wald doesn't make it, Zoom, Kalloy and other brands all make affordable cruiser-style handlebars that your LBS should have no trouble getting for $15 or so.
Good luck!