If the file manager doesn’t currently have the sole focus then I do not really see why remapping Cmd-Arrows would impact anything at all when the preview window has focus. I assume this type of stuff happens all the time on macs - it shares context more often than most other OS’s and the web browsers are a perfect example of this. Cmd-Arrow can change based on the context of having a text field with focus or have the webpage focused with no text field active. You can go back or forward a page when text is not being manipulated.
It’s really pretty intuitive imo.