We have faced the situation that you are facing currently and got creative with logshipping as there is no pause button for Log shipping.
We have implemented similar solution as a part of our Disaster Recovery fail-over testing -
Note: Below will not be clear as this site does not have any functionality for inserting a table from excel. But if you put below sequence in excel with header primary server and secondary server, it will be more comprehensible....
MAKE SURE THAT YOU TEST THIS BEFORE PUTTING IT IN PROD -- AS THE POST IS AS IS WITHOUT ANY RESPONSIBILITY OF DATA LOSS !!
ON Primary Server:
1) disable Log shipping (LS) job - Backup
2) Run LS Backup jobs manually
4) Kill all connections to database
5) Backup log(s) with norecovery (using T-SQL) - backup log db_name to disk = '\share\LogShip\db_name\db_name_YYYYMMDDHHMMSS.trn' with norecovery
12) Restore log(s) with recovery (Using T-SQL, Log backups that were created on step 10) - restore log db_name from disk = '\share\LogShip\db_name\db_name_YYYYMMDDHHMMSS.trn'
13) Run LS Backups jobs on Primary Server
15) Enable SQL Logins and sync them
16) Enable LS jobs
ON secondary Server:
3) Run LS Copy and Restore jobs manually to make sure all the t-logs have been applied to Secondary database.
6) Run LS Copy jobs
7)Restore database(s) with recovery (Using T-SQL, Log backups that were created on step 5) - restore log db_name from disk = '\share\LogShip\db_name\db_name_YYYYMMDDHHMMSS.trn'
8) Sync logins
AT THIS POINT DATABASES HAVE BEEN RECOVERED AND CAN BE ACCESSED
Now fail back --- after step 8
9) Kill all connections
10) Backup log with norecovery (using T-SQL) - backup log db_name to disk = '\share\LogShip\db_name\db_name_YYYYMMDDHHMMSS.trn'
11) Manually copy TRN file(s) to Primary Server (Created in step 10)
14) Run LS Copy and Restore jobs on secondary (check log shipping report)
15) Enable SQL Logins
16) Enable LS jobs