I think the maker or design of the uke has more influence on the tone in a uke than the wood does.
For example, LoPrinzi sopranos tend to sound like LoPrinzi's regardless of the wood used - though the wood will make sublte differences. I haven't had enough experience with the other sizes of LoPrinzi's to say that about the larger sizes.
Larrivees also tend to sound like Larrivees, although the woods used seem to make a fairly large difference in the ukes' tone - or maybe there's just less consistency among Larrivees. My spruce & mahogany sounds very different from my all mahogany that sounds very different from my all koa. But they still sound similar underneath it all - a kind of darkness in the third string that I love... yes, I think that's where the signature tone lives.
KoAloha's are always made of koa and they have a unique tone to them. Other koa ukes I've played didn;t sound like KoAloha's except for Kelii koa, which have a similar tone, though a bit more traditional than KoAloha's.
I've played 3 different vintage Martin's from the 20's and they sounded similar, though only one of them knocked my socks off. I played another one from the 50's and it sounded rather different - don;t know if it was the age, a slightly different kind of mahogany, or just that particalar Martin though.
And Ohana's, Makai's, and Mainland's tend to sound similar (they're all made in the same factory) regardless of the materials, though solid woods used do influence the sound and I do believe that spruce tops (and probably cedar) contribute to longer sustain, while hardwood tops tend to contribute to a punchy tone with more rapid decay in all ukes - but I've played many many exceptions to that rule too!
I've read that Mahogany is slightly warmer than koa, etc. etc. etc., but if I were to hear several ukes blindfolded, there's no way I could identify the wood used. I might be able to identify a LoPrinzi, a KoAloha, or an Ohana/Makai/Mainland... but then again, maybe not!!!! I find that certain ukes, regardless of price or make or woods used, really really appeal to me and are accessible even with my rather loudy playing technique...
Also, not even the best ukemaker or uke factory in the world can always make instruments sound great - consistency must be a hard thing to attain when you're dealing with organic materials. I've played a couple of very expensive and also inexpensive stinkers from makers that I normally like a lot. There was one very beautiful uke I remember in particular, handbuilt of all solid incredibly flamed loa, really tastefully done bling, just beautiful to look at... but the pits in tone. Wolf notes, many dead spots up the fretboard, oh it was a travesty of sound... It should have been hung up on the wall and never sold to a player... Never ever bought or played another uke from that maker again... But even my beloved LoPrinzi occasionally puts out a uke that isn;t stellar sounding, and LoPrinzi tends to be very consistent in my experience.