Is this a one time thing, or do you intend to keep it on this kind of schedule?
If you have a scheduled automatic download of new patch data for the Thursday after Patch Tuesday, then it would be a simple matter to then schedule a scan and deploy for the Second Tuesday of each month, and just schedule it after the upcoming patch Tuesday. January would use December's patches, February would use January's, etc. It sounds like you're looking for an offset of one Patch Tuesday.
There generally isn't a reason to delay by 3 weeks or more, since with those kinds of intervals, you can usually just change the scheduling itself to get what you need.
This would be a recurring monthly schedule and we are required to patch within a month of patch Tuesday. I just don't understand why the program won't let me go beyond 20 days from patch Tuesday? When I enter any number over 20 it's automatically changed back to 20 days. Due to other restrictions we don't start patching production servers until test servers have ran for one week with patches, also no patches are applied on Friday or Saturday nights. Based off of the calendar the closest interval between patch Tuesdays is 28 days, so theoretically we should be able to add delays up to 27 days.
When we were determining the max value to allow, we simply chose 20 days, since we hadn't yet had a situation where anyone needed anything more than that.
I would recommend submitting an feature request here: Shavlik Feature Request Form
Specifically, an enhancement to an existing feature. Those go to the Product Manager.