1. If the old cluster can be upgraded to 9.7, you may want to see if it's viable to upgrade ONTAP first. You may need to do a jump or two along the way because you're a long way back. It may be helpful to find the oldest version that the AFF300 can support (I'm too lazy to look that for up you) so you can meet in the middle.
2. Join the AFF300 to the cluster (add switches if the old cluster is a switchless cluster).
3. Once you've got the new nodes in the old cluster, simply vol move your data in the background.
4. Remove the old nodes from the cluster.
5. Upgrade the AFF300 cluster to 9.7P7 if you don't go there in step 1.
You can theoretically do the entire migration without any downtime at all.