Do try to find out which glue is recommended for the type of plastic used in the body. If you try a glue that turns out not to work, you've used up your only shot. You won't get a second chance. Something that sets hard is not enough. It must adhere to the plastic, and some plastics will shrug off some glues.
I agree with Kekani that it would not be worth paying for a professional repair, but if you can make a successful job of it yourself,then your attachment to that uke will be even stronger. My favourite uke is one I repaired myself. It had been written off as not worth bothering with, but the store gave it to me, and I fixed it.
Ukantor.
ps. Don't get attached to your uke by glue - that's painful!