Speed isn't the problem... time is. Long term travel in space will destroy the body. Even with artificial gravity, cancer is nearly inevitable. I am ignoring the mental and emotional issues.

Astronauts are extremely tough individuals.

Now, if we can figure out some form of suspended animation, that fixes many problems for long range travel.

I am much more convinced that our best way to leave our solar system will be without our physical bodies. Some form of synthetic or uploaded consciousness would be much easier to move around. After constructing a network, they could even be transmitted instead of shipped.

This is obviously in the range of science fiction but if we exist long enough, who knows.

The show, Pantheon, did a fairly decent fictional take on the idea.