Fuel costs would be horrific though.
I'm thinking the Niven approach might be better, since we don't have Bussard Rams yet. Sink a couple of fusion powered thrust tubes into Neptune's atmosphere and switch them on - same sort of principle as the Orion project, but self refueling. Take a while to get anywhere, but you certainly have the fuel and built in shielding. (Yes, I've been doing the calcs for this for a novel and it is feasible. Dangerous, but doable). Takes about 40k years to get to Barnards Star, where we know for sure there are planets, but computers don't care about time.