Sliding window partitioning?
If you are using FULL Recovery Model then change to SIMPLE (if you can recreate all the data in your warehouse database and thus don't need FULL) Then you won't need to make frequent LOG backups
If your database is already in SIMPLE then don't shrink the logs. They will just grow again. If you need them smaller then decrease the size of your batches - but, for me, I definitely wouldn't go down that route to save log space, I'd buy bigger disks!
If you need FULL Recovery Model then increase the frequency of your Log Backups. Every minute, if you have to. I'd worry if they were more than, say, 10 minutes apart.
But if you can TRUNCATE a table, rather than DELETE rows,that will save disk space. One trick, in case it applies, is if you have to delete most of the data in a table (most is probably "more then 60%" and if it is "more than 80%" it is probably going to be a good solution), is:
Create new, temporary table
(Don't allow any new inserts/updates)
INSERT into temp table the "rows to keep"
DROP the original table (including dropping any FKeys etc.)
RENAME the Temp Table to Original Name
Re-create and additional indexes / constraints / FKeys etc.
But sliding window partitioning probably better still, if that applies to your use-case.