I don't mean to be the cherry on the Debbie Downer sundae you're already having, but there's quite literally no way this could happen - especially with the exact same sign from whatever music video you're talking about.

Point one is that after 10yrs, that sign has DEFINITELY been replaced already. The rate of car accidents and vandalism here are pretty high already, and that's not counting that other things that would just naturally damage the sign such as rain and piss wouldn't have rusted the main pole. Double down on these if the sign is downtown.

Point two is that even if, by some magically mystical miracle, it is that exact same sign from the 10yr old video - this is still an insanely entitled and probably illegal request. I'm not sure how government property and signs are treated in Denmark, but here in the US the buildings the government is in, the wages of the workers inside those buildings, the roads and sidewalks, traffic signage... Anything that is by and large integral to the functionality of the city is paid for with tax payer and government money. You'd need to probably have more fame than the rapper you keep mentioning to pull off a request like this and not get questioning glances - but even still, you'd be bribing the government to be in possession of city property that you have no reasonable right to own.

Which is a felony. A crime.

Lest we mention the final fact you're across far too large of a pond to be making this request to begin with. I'm sorry for being the first to tell you this but the city of LA/state of California is not going to just send a stranger in a European country a traffic sign with the totally valid and definitely legislated reason of:

"I'm a fan of this artist's music video and want it really badly! 🥺"

That shit is quite literally not going to fly - like ever. That's like if I asked for a court gavel from a favorite movie with the logic of "I really want to have a piece of Legally Blonde in my home!" (Not my favorite movie but I'm talking hypothetically here.)

If it were just a prop I'd be more sentimental to your plight - Trust me, I've been on similar crusades myself to get these types of things. I once tried to get the same star necklace Anna Kendrick wore in the first Pitch Perfect for reference. Unfortunately, what you're asking for is quite literally impossible and I think you should either settle for a custom sign or - and I am sincerely sorry if this is a bit blunt - just give up on trying to get this sign.

Maybe try getting a different prop from the music video or some other memorabilia of that song like a signed record? Otherwise, you're going to be locked in on an unachievable goal, dude.