This is completely subjective but I often consider ukulele blues silly. It is like playing a funeral dirge with a kazoo or a slide whistle, or like Nina Simone singing Nicki Minaj songs: it just sounds ridiculous. However I consider myself a Roots musician and play a lot of blues-based things and here's what I do: 1. play in low G and 2. loosen the tension of the strings to make them less shimmery/chimey. I typically play in A tuning, 3 half steps looser than GCEA. That gives the timbre a little more bathos. Patently this only applies to chords, because notes are notes when finger picked. And again, I want to remind everyone this is very subjective. If a standard uke offers no problems to your ear, then go for it.
I was going to say much the same. What uke you choose to play the Blues sort of depends on what YOU think the Blues should sound like on your ukulele!
Muck like Ripock, I play a concert with Low G, tuned down to Low F. It's taken a while to learn to work that low-G string because it WILL get very boomy if you don't manage it. But, you can. You can either hit it lightly to not overpower a chord, or... as I've taken to doing lately, bump it with the thumb before striking the chord to give it a little bass-beat. Depending on what you're playing, of course.
FWIW, I picked out a nice Ohana CK-42. Redwood top for excellent resonance and sustain. I like it a lot!
There will likely be some trial and error finding the strings, setup and tuning that makes your uke work the way you want it to. My biggest issue usually ends up being finding a thin enough A string to keep it's "bendiness" on par with the other strings. I like things loose.
But, my uke would sound nothing like the one in the first post... at least not the way I have it set up.