I actually just installed a strap button and a guitar-style strap on my uke yesterday and I'm loving it!
I was a little apprehensive to screw anything directly into my uke, and after talking to someone at the music store I decided that gluing it on would be the best option. I used Gorilla Glue and just followed the instructions on the box. Used a rubber band to clamp the strap button on while it was drying and two hours later it was ready to go.
I was a little worried the glue wouldn't hold, but it seems incredibly sturdy so far, I played for a few hours last night and had no problems. I found it a lot of fun to play standing up with the strap, and loved being able to walk around while I played (although I'm sure my roommates did not). Maybe it was the novelty since I had mostly played sitting down before, but I loved it.
Oh, and if you're looking for a good uke strap I got mine from Souldier. They are all handmade in Chicago (local for me!), and they really look/work great. They sell both traditional Ukulele straps that hook into the sound hole (
http://souldier.us/CustomUkuleleStraps.aspx) and guitar-style "mandolin" straps (
http://souldier.us/CustomMandolinStraps.aspx).
I went with the mandolin strap and it fits perfectly on my concert uke (the strap is adjustable so it should work on any size uke). The ukulele straps looked good too, but I was just worried about ripping out the sound hole - an irrational fear I'm sure and I know tons of people use them, but still, I could see something happening due to operator error.
Anyways, sorry for the long post, but since I just did this yesterday I'm pretty excited about the results and thought I'd share...