Is the there a Way to Create a Constructor via Reflection that calls a Base Constructor. Specifically Entity Framework DbContext

I need to be able to call the Entity Framework model constructor of my model in 2 different ways. I either pass a connection string to my class, let's call it MyDbConnection, or I pass an existing EntityConnection (DBConnection) to my context, which comes from another application.

Everything is fine and works so far.

The problem I have, is: every time I want to use this custom way of opening my context in a new project, I need to define the 2 constructors in MyDbConnection which is quite a hassle.

Like this:

public partial class MyEntityConnection : DbContext
{
    public MyEntityConnection(string con) : base(con)
    {
    }

    public MyEntityConnection(DbConnection con, bool contextOwnsConnection) : base(con, contextOwnsConnection)
    {
    }
}

Then in my own implementation I do something like this (for the string overload):

public T GetDbContext() => (T)Activator.CreateInstance(typeof(T), _connectionstring);

and here is the problem. If I forgot to create one or both constructors, this would throw an exception.

Now I do know that you can modify the EF template to autogenerate those constructors, but im Looking for a Hands-Off Way to Archive this.

Some Way to Create the Instance of my Derived Class with a Constructor, that does not exist, and that Construtor should call its Base Constructor.

If there is a better Way to Archive this, im all ears.

private T GetExistingDbContext()
{
    try
    {
        EntityConnection econ = new EntityConnection(_internalMetadataWorkspace, _internalExistingSqlConnection);
        return (T)Activator.CreateInstance(typeof(T), econ, false);
    }
    catch (MissingMethodException)
    {
    }
    catch (Exception catr)
    {
        Console.WriteLine(catr);
        throw;
    }          
}

edit: fixed the Formating..Good God...First time Posting, sorry