Sql-server – Error during sp_refreshsqlmodule after altering table type

I am trying to add a column to a user-defined table type.
I have done some research and here is what I have now:

  -- First, rename existing table type to something else
EXEC sp_rename 'TT_MY_TABLE_TYPE', 'TT_MY_TABLE_TYPE_1'

-- Create the new table type
CREATE TYPE [dbo].[TT_MY_TABLE_TYPE] AS TABLE(
    [MY_FIELD] [varchar](20) NULL        
)
GO

-- Do a refresh of the SP/views so that the SP/views will refer to the new table type
-- Save the list of dependencies to a temporary table
SELECT  'sp_refreshsqlmodule ' + quotename('MySchemaName.' +object_name(referencing_id), '''') AS SQL_CMD
INTO    #TEMPSQL
FROM    sys.sql_expression_dependencies
WHERE   referenced_class_desc = 'TYPE' and referenced_entity_name =  'TT_MY_TABLE_TYPE';

DECLARE @sql NVARCHAR(1000)
-- Do a loop for the list of dependencies, use dynamic SQL to execute the SQL commands
DECLARE c_Cur CURSOR FOR
    SELECT  SQL_CMD
    FROM    #TEMPSQL

OPEN c_Cur
FETCH NEXT FROM c_Cur INTO @sql
WHILE (@@FETCH_STATUS = 0)
BEGIN
    EXEC SP_EXECUTESQL @statement = @sql
    FETCH NEXT FROM c_Cur INTO @sql
END

CLOSE c_Cur
DEALLOCATE c_Cur

-- Drop the old table type
DROP TYPE TT_MY_TABLE_TYPE_1

DROP TABLE #TEMPSQL

Unfortunately, while refreshing stored/procedures (their dependencies) to reflect the new type I am getting the following error:

Procedure sp_refreshsqlmodule_internal, Line 85 [Batch Start Line 0]
Operand type clash: TT_MY_TABLE_TYPE is incompatible with TT_MY_TABLE_TYPE_1.

I expect that the error is something else since all I did was adding one column to the new type.

Could you help me identify, what is the root cause of this problem?