Actually, even something as primitive as a NSWR (https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket) can reach a good percentage of the speed of light after basically processing a comet for fuel. From the Wikipedia article:
"The design and calculations discussed above are using 20%-enriched uranium salts. However, it would be plausible to use another design which could achieve 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."
Sure, not 99% the speed of light or continuous 1 g acceleration but IMHO good enough for an oversized nuclear squirt gun.
"The design and calculations discussed above are using 20%-enriched uranium salts. However, it would be plausible to use another design which could achieve 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."
Sure, not 99% the speed of light or continuous 1 g acceleration but IMHO good enough for an oversized nuclear squirt gun.