Change recovery mode and enforce a transaction log backup?
Yes in general that is a good approach.
As Shanky commented if you take a manual backup then the chain within BackupExec will be broken.


  If you have the ability to kick all the users on the server and can wait for the transaction log to be backed up by BackupExec then you will find it easier to start the work without involving another team.  Otherwise you will want to get the backup team to take the log backups before and after you have shrunk the data.

Only Shrink the database if you really have to reclaim the disk space otherwise leave it as it is. Brent Ozar has a lovely rant on shrinking, especially when scheduling it here and below is an excerpt from Paul S. Randal blog. The long and short of it is that it takes processing power to grow and shrink a log, this can be an unnecessary burden on an SQL Server.


  Shrinking the log is necessary if your log has grown out of control, or as part of a process to remove excessive VLF fragmentation (see Kimberly’s excellent posts on this here and here). However, shrinking the log should be a rare operation and should not be part of any regular maintenance you perform.