The best way to do what YouTube is doing would be with mod_rewrite. (And yes, YouTube is either using mod_rewrite or something exactly like it.) But before you build that, you have to ask yourself what you are hoping to achieve.
For example, let's say that you use mod_rewrite to convert this:
http://www.mysite.com/v/ZFMBIGAWa4e5cb83845429
to this:
http://www.mysite.com/secret/location/ZFMBIGAWa4e5cb83845429.flv
It's true that nobody will know that you're really storing the FLV's in a directory called /secret/location/... but so what? They can still access the FLV's directly with the original URL:
http://www.mysite.com/v/ZFMBIGAWa4e5cb83845429
mod_rewrite is great for lots of things but hiding content isn't one of them because, by definition, it's a pointer to the actual content!
Sure, it makes nice short URL's. And if that's what you want, then fine. But mod_rewrite isn't adding any security.
The best way to approach security is to identify a specific attack vector and then develop a way to prevent that attack. For example, finish this sentence: "I am worried that someone will (insert detailed attack technique here) and I want to prevent that."
