I suggest that you consider getting/using them later in the day. Morning is often, but not always, a good time to hit the bigger attractions. Probably the best time of day to do wand activities is at the end of the day (ideally, after dark). They are just much more magical after dark, IMO. Another good time to do wand activities is during the mid-day hours, when big attraction lines get long.
Though Universal isn't WDW, it still pays to zig when the crowd zags. Early in the morning, the crowd heads to the HP lands, even the folks who arrive after the early morning hours have ended tend to go there first, so mid-morning is a good time to be almost anyplace else. We like to use the early morning hours, but as soon as it gets crowded, we move to another area.
Mid-day = peak crowds, and thrill ride lines get long. That can be a good time to do short-line activities/attractions, like wand spells, shopping, taking in the details of the HP lands.
Universal is more compact than WDW, and the Hard Rock Hotel is just a few feet from the parks, especially the entrance of the Studios. I'm not telling you to avoid the delivery service, but returning to your room only takes a few minutes; just a world of difference from WDW if you are used to getting around WDW. Just maybe time your park re-entry until mid-day.
One last tidbit....if you do send the boxes back to the hotel (or opt to go to the parks without the boxes), I suggest that you either keep the wand map with you, or - perhaps even better - take some good (phone) photos of the map before you send off the boxes. If you opt to keep the original map on your person, perhaps consider putting it in a zip-loc bag to protect it.
