Ultrasound images acquired from different devices exhibit diverse styles, resulting in decreased performance of downstream tasks. To mitigate the style gap, unpaired image-to-image (UI2I) translation methods aim to transfer images from a source domain, corresponding to new device acquisitions, to a target domain where a frozen task model has been trained for downstream applications. However, existing UI2I methods have not explicitly considered filtering the most relevant style features, which may result in translated images misaligned with the needs of downstream tasks. In this work, we propose TRUST, a token-driven dual-stream framework that preserves source content while transferring the common style of the target domain, ensuring that content and style remain unblended. Given multiple styles in the target domain, we introduce a Token-dRiven (TR) module that operates from two perspectives: (1) a data view--selecting "suitable" target tokens corresponding to each source token, and (2) a model view--identifying ``optimal" target tokens for the downstream model, guided by a behavior mirror loss. Additionally, we inject auxiliary prompts into the source encoder to match content representation with downstream behavior. Experimental results on ultrasound datasets demonstrate that TRUST outperforms existing UI2I methods in both visual quality and downstream task performance.