Since TrendWear Ltd already has a revolving loan facility secured against its assets and the shareholder does not want to dilute their ownership, offering a mortgage over the business property is the best option. A mortgage would provide security for the investment without affecting the shareholder's ownership. Issuing or transferring shares (Options A and E) would dilute ownership, while offering additional fixed or floating charges (Options B and C) would complicate the existing security arrangement. 

Key Point: In investment scenarios, understanding the implications of different types of security is crucial, especially regarding the ownership structure and existing securities on the company's assets.