>> Is there anyway I can take a backup of the Primary server without disrupting the transaction log sequence numbers?
Use WITH COPY ONLY option in your Backup statement. A copy-only backup is created independently of your regularly scheduled, conventional backups. A copy-only backup does not affect your overall backup and restore procedures for the database.
BACKUP DATABASE ur_db_name
TO DISK = 'C:\ur_db_name.bak'
WITH FORMAT, COPY_ONLY;
GO
Above script would take a backup without breaking transaction log sequence