That's not actually a problem, because dangerous GRBs are simply not that common. Earth gets hit by one every day, but, that includes GRBs from very distant galaxies that are so weak when they hit us that they would not be any danger even to a completely unshielded person in orbit. GRBs of sufficient power to be an actual threat to people in a tin can is one/millions of years, at which point it's a propulsion problem again.
Yes, there are lots of things that could kill the ship on route. No, none of those are actually a significant problem compared to the basic "how to get there before everything breaks down from internal issues".
It's highly unlikely that a ship gets hit by a GRB.
On the other hand, general radiation gets worse the faster you go, so you need shielding either way. All you have to do is line the walls of your ship with a shit ton of water, which can be mined in space.
We don't have fuel sources that can run long enough for the trip, and deep space won't have enough solar radiation. We would need reliable mining spots along the way to replace metals made brittle by exposure or punctured by micro asteroids.
Even travelling at 1% the speed of light, stray hydrogen atoms become a problem. Not counting acceleration or deceleration time, that would be over 400 years just to get to the nearest star, let alone one with a habitable planet.
But that water needs to be encased in something, and your problem now becomes protecting the encasement.
Collecting it while usefully en route to another star system seems like it would be tricky from a delta-v perspective, but maybe the solution is to:
1) build a small worldship from an appropriate asteroid 2) fill your internal ocean in the outer solar system over the course of a generation or three 3) dive back down the gravity well for a gravitational assist from the Sun as you head to your interstellar destination 4) en route, slowly use part of your ocean as propellant, while living inside the rest of it as shielding
It would not really be about primarily traveling anywhere, just people settling this are with its immense resources over many generations, until possibly the ones on the furthest reaches would be able to make the jump to the next systems Oort cloud & slowly settling it down the gravity well, maybe even reaching the inner system eventually, provided something so tiny and sweltering would be of interest for them by that point. ;-)
IMHO this is actually much closer to how humans spread along the Earths surface. It was no like someone just get up and walked from Afrika to Australia. The various human group just expanded their habitat over time until they spread all over the place over many thousands of years and this would be similar.
https://en.wikipedia.org/wiki/Gamma-ray_burst :
> (GRBs) are extremely energetic events occurring in distant galaxies that represent the brightest and most powerful class of explosion in the Universe.
> The sources of most GRB are billions of light years away from Earth, implying that the explosions are both extremely energetic (a typical burst releases as much energy in a few seconds as the Sun will in its entire 10-billion-year lifetime)[11] and extremely rare (a few per galaxy per million years).
> All in all, a GRB within a few kiloparsecs, with its energy directed towards Earth, will mostly damage life by raising the UV levels during the burst itself and for a few years thereafter.
I'm guessing without an atmosphere protecting a ship it'd be a bit worse? But it's like winning a very bad lottery to get hit by one. I guess if you're traveling thousands of years in deep sleep odds get higher?