Re:
I can't comment on the whole ride but I would try to avoid as much as possible of the Otford to Wrotham stretch of Pilgrims Way between 7:30-9:00 on weekday mornings. It's narrow in places and cars come along much too fast - not a pleasant experience.
The alternative is to carry your bike up the steps leading out of Otford station; walk a few yards over the bridge that crosses the railway and take the path immediately on your right. Follow the path along until you get to a road (Tudor Drive); the path carries on, on the opposite side of the road, but off to the right, down the hill a little; then you follow it along until you come out in Dynes Road in Kemsing. Then just head east, over the crossroads, past the primary school, pub, fields of sheep. Turn left at Heaverham and go up the hill until you reach Pilgrims Way. You can see the route clearly enough on Google maps.
At the other end, I personally prefer the route via Wye: cycle route 18. It gives a more pleasant approach to Canterbury, beside the river. However, that's deviating from Pilgrims Way again.
I'll be interested to hear how you get on.