Will a Transactional Replication break the LSN chain in my backups
I did look at log shipping to keep the copy up to date but this will
  break the LSN and render my backups unrestorable (Log backup every 15
  minutes).


Technically, no they won't break the LSN. It simply means when restoring you would have to coordinate restores with both your managed backups and your log shipping backups. While this is a nightmare from a management overhead perspective, it won't actually break your LSN chain like say changing the recovery model would.


  I reasonable confident that a Transactional Replication will fit the
  bill working from the Distribution Database and leaving the source
  unaffected but I can't find a definitive confirmation of this.


Transactional Replication reads the transaction log and writes the transactions affecting tables marked for replication into the distribution database for distribution to your subscribers. This does not mark the transaction log except to mark those transactions it has already processed for future runs of the log reader agent to avoid duplication of work.

Transactional replication will not impact your managed backups, break the chain or affect the recoverability of your database from managed backups.