How to transfer files from SD card to Windows formatted external drive through Mac WITHOUT reformatting?

I'm having a very frustrating issue. I want to transfer GoPro videos to my external while on vacation, and I have a Mac laptop. The goal is to access them on my Windows PC when I get home. It seems that my Mac will read files on my Windows formatted external but will not write. If I format for Mac, I can write but then my PC won't recognize the files. Any way around this ridiculous problem?

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