I'd be wary of messing with it before seeing if you can get redress from the supplier who packed it badly.
If the supplier was a reseller, not the manufacturer, and if the damage is definitely due to postal mishap, then you may not be covered under warranty. But I'd still take the time to ask the manufacturer's rep.
I'm not familiar with the brand, so excuse my ignorance here... If it is a cheap, laminated Chinese uke at the level of Makala or Mahalo, then if it were mine I would happily attempt a careful repair with LMI or Titebond (but not their awful liquid hide stuff) - or a screw fix as suggested. You'd have little to lose.
If, on the other hand the uke is a step up - perhaps equivalent to a good Kala, or a Mainland or Ohana, or better - then I'd say to heed Mr Turner's words. Free advice from a respected luthier is always worth listening to.
If the uke is worth the cost of a proper repair then get a pro to do it.