SQL Server Compact 4.0 – How to Query Database Content

After OP's Edit to the question :

Try to use Visual Studio 2010 SP1 + VS Tools for SQL CE 4

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SQL Server Management Studio 2008 R2 supports for SQL Server Compact 3.5 database. (ATTENTION from SSMS version 2012 and newer, Sql Server Compact databases are no longer supported by SSMS; You must use SSMS 2008 R2 or OLDER)

Note : SQL Server Management Studio cannot open SQL Server Compact 4 files, only SQL Server Compact 3.5 files.

Click View >>Toolbars >>SQL Server Compact Edition Editor as shown.

Additionally, refer to SQL Compact 3rd party tools and

SQL Server Compact Toolbox on Codeplex - It is a Visual Studio add-in and standalone app , for managing all aspects of your SQL Server Compact database files.

MySQL is my area of expertise and SQL Server isn't... but it looks like the answer is you definitely can manage the migration with SSMA on a client PC, but it also appears that both your client machine and the SQL Server need connectivity to the MySQL server. Reading between the lines, it sounds as if the client machine might use its connection to MySQL to discover the schemata and then something from the server-side components installed on the SQL Server would subsequently connect directly to MySQL to fetch the actual data rather than the data being actually piped through the client machine where you're using SSMA.

To use SSMA, you first must install the SSMA client program on a computer that can access both the source MySQL database and the target instance of SQL Server or SQL Azure. Then, install the MySQL providers (MySQL ODBC 5.1 Driver (trusted)) on the computer that is running SSMA Client Program.

^{— http://technet.microsoft.com/en-us/library/hh313129.aspx}

In addition to installing SSMA, you must also install components on the computer that is running SQL Server. These components include the SSMA extension pack, which supports data migration, and MySQL providers to enable server-to-server connectivity.

^{— http://technet.microsoft.com/en-us/library/hh313121.aspx}