Measure your spindle length on the Sugino BB; if you can, measure the distance from right end of spindle to right side of BB housing (on the frame). Taper end size of the Sugino should be pretty close to Campy. Campagnolo spindles varied, quite a bit, depending on road/track/triple of course, but also on size of bearing balls used (3/16" vs 1/4"), and thin cup vs thick cup (later) with rifling in spindle hole to keep dirt out. Sugino spindles came 109 (track), 113 (Suntour Superbe) and 115 width, too; to complicate matters even more. I've seen some Sugino cups with a neoprene dirt seal, and some without -- that may affect the cup thickness. Check out what you have, and post back.

The S-A shim is about 1 mm (maybe 1.5 mm = 1/16") thick, and steel. Should fit both freewheel and fixed cup. It shouldn't create a problem to use a spacer on the fixed cup, since English is left-hand threaded (the correct way to do it) and will tighten with precession. Some places sell aluminum shims; I wouldn't use one of these, if I could avoid it.