It's definitely doable. The "'Momentum Limited' Orion" concept[0] has a delta-v of 10,000 km/s, which should be plenty enough to catch up to either of the Voyager probes. It can also carry ~25,000 tons of payload - that's a lot of spare parts!
[0] https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls...