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!
If you're okay with just a flyby of the Voyager probes though, then you can use a laser sail. Breakthrough Starshot[1] is aiming for 60,000 km/s of delta-v. Lightsails have already been demonstrated several times in practice[2].
science4sail|1 year ago
[1] https://en.wikipedia.org/wiki/Breakthrough_Starshot [2] https://en.wikipedia.org/wiki/Solar_sail#Projects_operating_...
chuckadams|1 year ago
Solar sails, yes. Starshot needs a Death Star Laser that makes the NIF look like a cat toy.