Rather than trying to get cron jumping through hoops, it would be much easier to invoke the script via cron every third weekday then inside the script test if it is the first week and bail if not. Get epoch seconds from time, calculate epoch seconds a week ago by subtracting 86400 * 7 seconds then use Time::Local::timelocal() to get the month number from each one; if the month isn't different you are not in the first week.

I hope this is helpful.

Update: A general note of caution with this approach, if your cron job is running an hour either side of midnight then beware of daylight savings changes in case they throw the calculations off. I've been bitten on the bum by that :-)