The A61 route is not too bad, depending on the time of day that you ride it. Once over the A1 you are going against the majority of the traffic.
However I would, for preference, go Ripon, Sharow, up to the roundabout at the A168, turn towards Rainton, go through same, heading for Topcliffe. Go straight through Topcliffe and on to Dalton, then follow the road to Thirsk (and you will go past a 10th century church and the house where I grew up).
Can't help you with the other route, though.