MongoDB delayed member replication mechanism
The implementation is as per your first suggestion: a delayed secondary applies operations from the source oplog based on the delay. Your concern is also valid: if the source oplog period is insufficient to cover the secondary delay, the delayed secondary will become stale and require a re-sync.

A delayed secondary will help you with some data recovery scenarios (for example, a collection drop that hasn't been applied yet), but for more comprehensive recovery options I would consider a continuous backup solution such as MongoDB Cloud Manager (or MongoDB Ops Manager, which is the on-premise equivalent). Cloud Manager Backup provides continuous backups with queryable snapshots that allow you to preview and restore a subset of data. Base snapshots are taken every 6 hours by default, with a customisable snapshot interval and retention policy.