Testing a Class with a Static Class/method dependency

So I have a class that looks like this:

public class MyClassToTest()
{
    MyStaticClass.DoSomethingThatIsBadForUnitTesting();
}

and a static class that looks like this:

public static class MyStaticClass()
{
    public static void DoSomethingThatIsBadForUnitTesting()
    {
        // Hit a database
        // call services
        // write to a file
        // Other things bad for unit testing
    }
}

(Obviously this is a dumbed down example)

So, I know that the second class is doomed when it comes to unit testing, but is there any way to uncouple the MyClassToTest class so that I can test it (WITHOUT instantiating MyStaticClass). Basically, I would want it to ignore this call.

Note: Sadly this is a Compact Framework Project, so tools like Moles and Typemock Isolator cannot be used :(.