A Campagnolo Gran Sport would be period-correct and vastly superior, with the benefit of not crashing into the spokes if the cable slips or breaks.
Disclosure: I had a Sturmey-Archer 3-speed AW hub with a 14-16-18-20 1/8" cogset. Frustrated by having only of the gears and lousy shifting, I upgraded from a bandspring Cyclo to a Gran Sport, which worked like a champ.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069