Fastest way of restoring log shipping of multiple databases
Below is the approach that I would take :


Stop logshipping jobs on both primary and secondary database servers.
If a FULL Backup job is run on the primary server then you have to initialize logshipping by restoring the latest full backup and a diff or subsequent log backups.
If a full NON COPY ONLY backup is not run on primary server, you can follow the rest


Take   differential backups of the databases on primary server.
Move all the backups to the secondary database server. You can use Robocopy or powershell to do this.
Restore the DIFFS on the secondary server using norecovery.
start logshipping jobs on primary and secondary.
At this point your logshipping should be resumed.