Agreed. There should be no problem with them sitting for 2-4 weeks. Unscrew the needle while it is still in the sterile wrap, then pull out the syringe and attach it to an 18g needle stuck in the vial, draw out your amount, return the syringe to the wrapper and twist-lock the covered needle in place. Total exposure is negligible if your working environment is reasonably sterile. Leave the 18g in place, and fill one syringe after another until done. For ED shots, there should be no trouble loading a few weeks, then they are all ready for action, just pop off the tip.
And for those who think this is compromising sterile procedure, the exposure to the air is no more than the exposure of any needle to the air before a shot - i.e. as perfect as it is going to get short of walking around in a bubble-suit filled up to the neck with anti-bacterial and anti-fungal preservatives.