I'll vote contrarian and say to reuse the spokes - especially since they haven't given any problems in the past. I cycle under conditions that are kinder to the rims (very little rain and almost all on-road), so I get well over 50 kmiles before the brake track gets worn out. I've still reused spokes for two or three rims without any issues - so the spokes went for about 200 kmiles. At only 6 kmiles on the OP's spokes and none broken I wouldn't have any qualms about reusing them. (But I would carry a few spares if going on an extended tour.)
To keep all the spokes in the same position in the hub and minimize stresses it's easiest to tape the new rim alongside the old one with the valve holes aligned. Then move the spokes over to the new rim one at a time.