Tran Log file growing even after log backups and Log shipping configured

I have log shipping configured for a database in sql server 2005 with below details:

A) Database X hosted on primary: Log backup every 1 hour as scheduled in LS Backup job:

Data file: 40 GB and Log file: 15 GB (Initial file size:13,701 MB with 10 % increment growth)

B) Per Log shipping that Database X is hosted on secondary as X_DR whose log file is also the same and due to shortage of space on this server we get continuous alerts for low disk space.

Therefore to control this Log growth can someone please guide me how to proceed:

1) Analysed the log file usage on primary and found that for that duration of one hour where log backup will occur, the max log used from its define size is 3-4%! So does that mean give amount of log space is not being used? if yes can i change the initial size to approp value in live prod DB as of now?

2) If point 1 is not valid should i go with shrinking log files as they grow quite large. Dont want to use the option 2, but kindly help me with any suggestion/solution

Thanks!