While radiation is a serious problem at relativistic velocities, you're a bit too pessimistic: The most immediate problem is the interstellar gas, which become

While radiation is a serious problem at relativistic velocities, you're a bit too pessimistic: The most immediate problem is the interstellar gas, which becomes hard radiation at relativistic velocities. However, ~2cm of aluminium shielding are enough to reach 0.3c, and with 1m of water, you can reach 0.5c. For higher velocities, magnetic shielding coupled with a metallic electron stripper is probably a more pragmatic solution.