If it takes 10,000 years, what's the point of sending people? 10,000 years is longer than the whole of recorded human civilization; even assuming you could keep the crew alive in hibernation for that long (I'm quite sure you can't), what would they do when they got there? They'd have the rusty tub they came in, and... nothing. If they managed to land safely on a planet that happened to have a breathable atmosphere and all the natural resources necessary to build a successful colony, I suppose it's possible they could succeed, but how would we even find such a suitable destination for them? Far more likely that they'd land on a frozen rock and be confined to the ship until they either suffocated or starved to death.
Unless, of course, during that 10,000 years our technology and understanding of the universe advanced to the point where we figure out how to do FTL travel in some way, so when the colonists finally arrive, we're already there to welcome them.
Let's see if we can send a few unmanned probes to other solar systems before we try it with people, shall we? At this point we can't even do that.