Schnyder beat U.S. qualifier Meilen Tu 6-4, 7-5.
The left-handed Schnyder was the 2002 Charleston runner-up to Croatia's Iva Majoli.
A second-round upset Tuesday saw Colombian Catalina Castano beat fifth-seeded Czech Nicole Vaidisova 7-5, 6-2. World No. 14 Vaidisova, 16, has now lost two straight and four of her last five matches after opening her season at 8-2.
In other second-round play, Spaniard Lourdes Dominguez Lino defeated Puerto Rico's Kristina Brandi 6-4, 6-4.
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