Do I need region-specific trust signals (e.g., EU cosmetics regs) to convert?

As an e-commerce brand selling products internationally, I'm increasingly aware that different regions have unique regulatory requirements and consumer trust expectations. I want to understand how including region-specific trust signals like certifications, compliance badges, or localized quality indicators might impact my conversion rates. Specifically, I'm curious about whether displaying EU cosmetics regulations, FDA compliance for health products, or organic certification matters when selling across different markets. How can I strategically leverage these trust signals to improve customer confidence and potentially boost conversions?