Of note is that I believe California allows you to register extremely old plates so long as the year of the plate/sticker is the model year of the car. So a 1968 CA plate can be legally registered in California...but only on a 1968 car. So, assuming you drive a modern car, it could cause problems if you were to visit California, or any other state that is near enough to CA that a cop might be familiar with their laws.
As you already concluded, the safest thing to do is just leave the plate in Florida.
You have at least two problems, if you visit California:
1) Some newer (vanity, I believe) California plates are the same colors as the plates issued 1963-8
2) California is a two-plate state and displaying different front and rear plates might very well confuse law enforcement and trigger a stop, even if it turns out to be completely legal.
I don't know if "some lumphead from Florida trying to be cute" is regarded as "probable cause or reasonable suspicion", but I know that I wouldn't want to have to try to contest the validity of the arrest, if the officer finds any subsequent violations of any laws. So, if you decide, despite my advice and that of others to drive with it on your car, please make sure that you don't provide evidence of any other violations. For instance, throw your old beer cans in the recycle bin before you leave the party. Keep any open liquor bottles resealed as much as may be, in a suitcase in the truck. Make sure that any legal marijuana is clearly identified as purchased in state (and thoroughly clean your ash trays), etc. Basically, don't break any other laws, no matter how chickenshit.
I'd say, keep the plate and use it when you show off your car in a car show or use the car in a music video or whatever. I wouldn't drive with it on the road much outside of Florida.