Analyze the concept of cognitive load theory and its application to e-commerce User Interface (UI) and User Experience (UX) design. Explain how extraneous, intrinsic, and germane cognitive loads influence a shopper's ability to make purchasing decisions. Propose theoretical strategies to minimize cognitive load during the product selection and checkout phases. Discuss the relationship between reduced cognitive load and increased conversion rates, citing the principle of 'paradox of choice' where relevant.