One thing a lot of people overlook is the time a queen spends with her nuc or package after it's made up, & before it's received. "3 days after you got them" probably means 4-5 days, unless you picked them up on the spot, the moment they were made up.
Beginners tend to be a bit intrusive (naturally), but letting the queen loose after 4 or five days shouldn't be all that risky if you are gentle about it. If I were to make a list of things beginner's should do, one of the first things would be find a chair, place it by your new hive(s), find another good bee book, and start reading. When you get the urge to inspect you hive, read another chapter first. The bees will be OK for that much longer.
Much can be determined by observing a new undisturbed hive from the outside. Inspections are necessary, and releasing a new queen isn't a crime. She'll probably be fine, but her chances will be better if you spend more time relaxing with a good bee book than disturbing your new friends.
I just released two of my recently hive package queens, yesterday. Of four, two had already joined the hive, while two had access but were reluctant to leave their now crowded cage - packed with bees that had eaten the entire candy plug. These queens came without attendants, as they were in a 3 lb package. That the cage was packed with bees & queen meant her departure was both available and imminent. Rather than closing them up and coming back later to disturb them yet again I chose to release the queen right then.
I gently pried up the screen staple, sprinkled a little syrup ( from the feeder jar) a few drops on the cage, & maybe an oz onto the frame tops. I've recently read that some other respected Beeks do not advise this, for valid reasons - risk of drowning both queen & bees, but in my dry climate they seem to just love it. It seems to sooth and distract them while the queen quietly slips down between the frames. As it has done many times in the past, it did again this time - queens in. By the time I got the inner cover back in & the feeder jar back in place, I could hear the dull "what's the disturbance" roar" subsiding to the soothing "ahh, that's better" hummm.