I recall the last time a repair shop recommended a transmission fluid change. I was astonished. The fool was not aware my car had manual transmission!
Yes, your service manager has a boat payment due. That doesn’t mean he is right or that he is wrong about your car. And nobody can predict the result on your trip. My guess? Take your trip as-is, everything will be OK. Transmission fluid is supposed to look a bit dirty after some use. But if this is really going to prey on your mind, have someone do the job (not necessarily the dealer).