SQL Server 2008, standard log shipping setup (well, using redgate, but it is a pretty normal flow).
On the replica, the log file is pretty big.
Wondering if on the backup/replica servers it is OK to shrink the log in some way?
The log file on the replica follows exactly the file on the master. They can't be different. You can shrink the master and the replica will automatically change to match.
Running DBCC SHRINKFILE without the TRUNCATEONLY option on the primary will propagate the change to the secondary once the log is applied, so it will shrink to the same size..