Can I specify the default backup location for non-automatic backups?
No, it's not possible to specify a default location.  The best way to do this would be to write a shell script (which specifies your location of choice) to handle your backups.

You can have DB2 remove old backups (using the AUTO_DEL_REC_OBJ database configuration parameter with proper values for NUM_DB_BACKUPS and REC_HIS_RETENTN), but that will only occur after a successful backup.  

So you'll need to ensure that there is enough space for the backup to complete successfully.