Here's where I taped it. I also taped it inside as well.
You'll be absolutely fine. Airports have, to put it simply, seen much worse.
Assuming that, depending on what kind of break is going on there, fragments and/or debris won't come off of it (or harm anyone handling it), it will pass right through without a hitch.
Bear in mind that it'll have other cases/weight on top of it etc during handling/flight, so assuming that bit of tape is fine at keeping it together, no worries.