Dempsey, who won the world title in 2009 and Olympic silver last summer, won his opening race in Buzios before finishing seventh in his second to place seventh overall.
Fellow Brits Elliot Carney was eighth and 14th for 23rd overall while Tom Squires was 19th and 26th for 44th after the first two races in the men's fleet Brazil.
Meanwhile Olympic bronze medallist from Beijing 2008 Shaw was the most consistent of the Brits in action, finishing fifth and then third in the two women's fleet races to place third overall.
Charline Picon leads with Eugenie Ricard second while fellow Brits Izzy Hamilton was 25th and 20th for 22nd with Claudia Carney seven places back after two races following a 35th and a 25th.
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