EF 6 programmatic Migration with custom connection string

I have an EF6 code first implementation with migrations enabled and a single initial migration. I created a method to programmatically run the migration that looks like the following:

public void RunMigration()
{
    var migrationConfiguration = new DataAccess.Migrations.Configuration();
    var migrator = new System.Data.Entity.Migrations.DbMigrator(migrationConfiguration);
    migrator.Update();
}

When I got to testing I have several configured connection strings in the App.config. My Question:

How do I tell the DbMigrator what connection string to use?

update: I suppose the catch is doing this without extending DbMigrator.