As you noticed, Sunday is day zero in cron ... but day seven in "date +%u".
Just for interest "date +%w" gives the Weekday numbered the same way as cron.
Ps. We need to know whether "the script" does anything other than sit there idling and fire off another script at 10:00 on weekdays. How accurate does 10:00 need to be? Would up to 59 seconds either way matter?
Downside is if the system is re-booted, put in single user mode or your script dies the job won't run. Perhaps you could add something to your .profile so when you login it checks the script is still running and fires it off again.
Another thought, do you have access to run at jobs?
while true
do
CURRHOUR=`date "+%H"`
CURRDATE=`date "+%u"`
if [ $CURRDATE -lt 6 ]; then
if [ $CURRHOUR -eq 10]; then
// program
sleep 3600
else
sleep 30
fi
fi
done
#to run : $ nohup ./daily_run.sh &