Is my upgrade path from 1.5.2 to 2.1 correct?

I'm currently using a single ES node cluster which is currently on v1.5.2.

In order to upgrade to 2.1.x do I simply shut the node down, run yum update elasticsearch (with the Elasticsearch 2 repo enabled) and then restart the node on completion?

I've checked the configuration and updated it where required, The migration tool runs and comes back without issues.

We have vast amounts of backed up data in snapshots (taken at v1.5) which have since been deleted from the cluster. In the event these are needed in the future will these restore without any changes onto 2.1.x?

Yep!

As long as there is nothing that may conflict with changes in 2.X, ie things that may be caught with the migration checker.