No you can't have California plates on a car registered in Nevada. It's like having Nevada plates on a car registered in California. I don't think cops are looking to pull over people with out of state registered vehicles and you'll have to explain why it has California plates and you have a Nevada driver license if you're pulled over and someone asks.
If it was MY FJ45 I'd hang the plates in the garage, get it registered and move on. It's smog exempt so I don't see the point of keeping the California plates other than to let everyone know you came from California.
I kept the vintage Colorado plate on the front of my Early Bronco, and haven’t been hassled about it yet..... It’s got the Nevada plate on the back though, and I’m sure they could have an issue with the Colorado plate if they wanted to