I have two ukes with buttons - my custom Donaldson, and my Ohana Concert. Both have pickups, hence the button on the bottom, and both have buttons at the heel - Rick Turner installed the one on the Donaldson, and Mim did the Ohana. I use Uke Leash straps for both (Thanks, Lori!) with leather button adapters.
But the funny thing is, I only use a strap when I'll be playing a 1+ hour gig. When I'm doing that, I have to move around a lot, sitting and standing, because of the steadily increasing arthritis in my back, hip, and knee, and sometimes I need both hands to adjust a stand, a mic, or song sheets.
If I'm at a jam, or song circle where I'm going to be able to sit, or a shorter duration gig, I don't use a strap at all.
The only time I've ever dropped a uke was when I was doing the silly behind the head thing, and lost my grip. the finish was a really thick gloss, and it chipped at the binding. No change in sound, or playability, and if you aren't looking for it, you don't see it. It was a learning moment, and since I'm not Roy Smeck or Stu Fuchs, I don't screw around like that anymore.
So, to get back to the reason for the thread, I say that if you are getting a strap button, get them both. When you need to use them, you will be glad you did. Years back, while playing guitar, I noticed that when I tied the strap to the head/neck, some of my guitars sounded different. It turned out that the intonation was changing with that slight bit of weight, and I had to retune constantly. While the weight of a ukulele probably won't do that, I'm not going to bother finding out.
-Kurt