As the peak neutron flux and fission reaction rates would occur outside the vehicle, these activities could be much more vigorous than they could be if it was necessary to house them in a vessel (which would have temperature limits due to materials constraints).
However, it would be plausible to use another design which would be capable of achieving much higher exhaust velocities (4,725 km/s) and use a 30,000-tonne ice comet along with 7,500 tonnes of highly enriched uranium salts to propel a 300-tonne spacecraft up to 7.62% of the speed of light and potentially arrive at Alpha Centauri after a 60-year journey.
[1] "NSWRs share many of the features of Orion propulsion systems, except that NSWRs would generate continuous rather than pulsed thrust and may be workable on much smaller scales than the smallest feasible Orion designs (which are generally large, due to the requirements of the shock-absorber system and the minimum size of efficient nuclear explosives).
"[7] The propellant used in the initial design would contain a rather large amount of the relatively expensive isotope 235U, which would not be very cost effective.
Zubrin claimed in his design that the apparatus was created so that the liquid flow rate or velocity was what mattered most in the process, not the material.
The vessel's exhaust would contain radioactive isotopes, but in space, these would be rapidly dispersed after travelling only a short distance; the exhaust would also be travelling at high speed (in Zubrin's scenario, faster than Solar escape velocity, allowing it to eventually leave the Solar System).
However, this is of little use on the surface of a planet, where a NSWR would eject massive quantities of superheated steam, still containing fissioning nuclear salts.