@Charles, you can use the sim redirector ">" file in ShellExecute, but using cmd.exe, which is an interpreter of Windows commands.
try this sample
ShellExecute(0,nil,'cmd.exe','/c MySqlDump.exe -u user1 -ppassword dbName > TheOutputFile.Sql',nil,sw_normal);
Other options are using channels, you can find a very good example in this link .