Shirking of Log file on Primary Server of Transaction Log shipping
I have a database with size 200 GB Total(mdf+ldf) and Log file(ldf) with 50 GB and 99% unallocated space in ldf file i.e. not being used at all.


Leave it as it is, the space would eventually be utilized without any autogrowth and that would really help your SQL Server transactions, so just DONT shrink.

FYI


You can shrink log files on primary server
DONT change the recovery model this would break logshipping. Yes you can  shrink without changing recovery model
The log file will eventually again grow so there is no sense in shrinking.
You may use NO truncate but normal shrinking would just do fine. This is just to answer your queries I would still say do not shrink.


Further reading Why Does Transaction Log file Growing and Runs out of the Space