Best practice for doing DB maintenance for databases used in Log Shipping:
Setting to simple mode will break the log chain, so that is out for LogShipping. Development suggest to maintain the database to whatever degree it requires and ignore the fact it is log shipping, just take more frequent tran log backups during index rebuilds\reorgs. One thing you can do is run integrity checks (checkdbs) on the secondary database to take some load off the live database
But at the same time you may find you need to change Full recovery model to Simple because reindex on a database with TB of data in a Full recovery mode will enlarge the transaction log dramatically.