In this manuscript, we propose a motion strategy for manipulating strings with unknown properties. Our approach iteratively refines its motion generation based on parameters estimated from observed string behavior, without the need for real-time feedback. This strategy has been shown effective in achieving several motion objectives using uniform strings of similar lengths. In this research, we improve upon this strategy by addressing the challenges posed by varying string lengths and non-uniform strings. For this, we utilize a non-uniform string model and address various string properties to demonstrate the feasibility of our proposed motion strategy. Experiments conducted with different string types and lengths (between 300 to 610mm), including some with non-uniform mass distributions, demonstrate our method's effectiveness. Results show that our proposed method functions effectively with various kinds of strings, regardless of length and mass distribution, without requiring precise model parameters. Unique to this approach is its ability to adapt to various string characteristics through parameter estimation and motion generation, significantly reducing the need for real-world manipulation trials. Our findings illustrate the potential of our method for use in advanced robotic applications that require handling deformable objects.