It may/will speed up to install SQLyog on one of the server machines. I cannot tell how much but it eliminates one network connection.
Also the speed issue may equally much (or more) be an issue with ODBC/the ODBC driver (and how efficiently it uses a network connection) than with SQLyog itself. Is SQLyog slower when reading the data than other programs connected using ODBC (Access, Excel for instance)?
If you want us to comment more in detail on your speed issue, we need a test case or at least some numbers and other details like table structure, KBs/MBs transferred, number of rows, whether you use any 'advanced' options (WHERE, TRIGGERS), the type and speed of network etc.
You are welcome to try all scenarios while testing this using the copy that you have. Please share your findings here!