I use a strap similar to the one Jake uses. I only use it on my KoAloha Tenor. I purchased the uke last November while in Hawaii. It was a scratch and dent and the price was really good. There's a slight ding on the headstock. I didn't want to install a pickup or strap buttons so I bought an appropriate strap. It takes some getting used to, much different feel than using a traditional strap. I don't feel comfortable playing with this strap while standing.
Whatever works for you is correct.
I hate the thong with a clip type of strap. The tenor uke ALWAYS tries to do a face plant if I forget to hold it tightly to me with one of my arms. Two managed to do so. One, a Fender Nohea, when the plastic clip broke. The other, a Pono ATD when I stood up and, yep, forgot to grab it as I did so.
I used to play with a strap button on the bottom and tie the other end around the headstock. First with a shoelace and later with a mini strap and the strap went over the button on it. (A real metal button, not a bulbous peg.)
After a year, I was getting more and more annoyed with having the strap attached at the headstock. It seemed to get in the way a lot. So, I installed a button on the side of a heel and started playing with the strap attached at the heel and the butt. Much more gooder. Now every one of my ukes has two buttons, or a heel button and a Jack/button.
I like to use 2" guitar straps on my tenors. I tried the 1.5" Ukulele straps, but they bother my shoulder too much. Besides, there are way more cool looking guitar straps than there are ukulele straps.
Jake's strap clip did not distract or flash much when I saw him in concert. It was a matte brass. The glare from his gloss Kamaka was far worse.