My first three ukes (bari and 2 tenors) came secondhand with dual buttons pre-installed by HMS.
I have never used a strap before on my mando-family instruments, but found that one helped to stabilize the ukes' much lighter bodies, which wanted to move around much more than the aforementioned instruments ever do. That goes for sitting as well as standing, to my surprise. But my fourth and final uke, a Tiny Tenor, has no buttons, and I find that its unique, more mando-like shape is easier to hold onto without a strap.
I don't think I'd ever want to attach a strap anywhere on the headstock of any instrument. I don't know if it would get in my way physically, but I think it would annoyingly intrude on my peripheral vision.
bratsche