I’ve seen a few wooden watches use wooden dowels for the connectors, but they are not for every day wear. BUT I’m sure it can be made to work.
I don’t think “U” shaped clips are the best way to go for this style. They work in stretch bands and in some more inexpensive bands, but as someone who repairs watches for a living, I don’t like them. Screws look better, are easier to repair and hold longer. BUT that’s just my opinion. 
If I were to go with wooden dowels I wouldn’t do any physical clip. But maybe try doing something to make the wood maleable (vinegar vapors I think?) and then hit the ends so they flare out.
It would be tricky since you want to only modify the dowel, but need to do it in place. But it should be possible to accomplish from what I have seen done to wood before. The major question would be if the wood would maintain the modified shape once it dries. I am far less certain about that happening.
If the wood shaping doesn’t work, then finding pins which are reasonably well hidden would be the best I think. I had contemplated designing the wooden dowels to be essentially staples (so one part goes through two tracks), but that seems like it would add considerable bulk along the sides of the bands (though someone artistic could probably make it still look nice).
Just trying to think of ways to keep it all wooden - would this idea work at all? Using two pieces like this slipped perpendicular to each other and “click” together when the indented legs go into the square opening. Now the top would still only be 2 dimensional ( the cap or part visible. Would also have to be thin and small so probably wouldn’t be strong enough… Sorry for the drawing - still haven’t had time to try and practice with any 3d programs. Just kind of “thinking” out loud.
Might be too tiny to use on a watch link, but I can sure use the idea for other stuff! Thanks for posting it. 
One of the nice things about having a laser is that making new bits is easy. So maybe just bond the pins and the outermost links and remake if/when you need to? Might take less time than complicated reassembly and disassembly.
Meanwhile, there are also a few hundred years of wood puzzle joints to explore for holding things in place…
Boy, ain’t that the truth! Been looking at quite a few from some earlier links. (I’m still designing for mortise & tenon with a spot of glue though - I hope to graduate to snap-locks one of these days.) 
Clever! That would definitely be worth a try.
This would work with different material, but with 1/8" being the thinnest I have, that’s how big the holes would have to be on the links–otherwise I’d do a test cut on your design. The holes are currently ~2mm, but a material if that thickness could work. Clever, I hope I see you cut it out and post it later 
Nice, I could see this iterate into very very nice with the right hardware and exotic wood.
I was thinking the same thing…I would undoubtedly impale myself on the protruding screws at that length…lol
I have a Fitbit HR that emancipated itself from the band. thinking of making something out of leather for it once I get my GF.
I might just make the housing leather and use your band now. Hasn’t torn all the hair off your arm or anything has it?
Not at all, and the bolts haven’t poked me either.
How about Weaving the links together with round elastic cord? Bracelets would be a fun, inexpensive kids project using some scraps and avoiding the cost of the connecting bolts. The edges of the outside links could even be elongegated to have less exposed elastic showing.
Sounds like an option to me. I did consider doing something like that, but
I happened to have the bolts and thought “why not”. Please try it out and
post the results!
Is the material too thin to handle counterbored hardware?
A fun early project when I do get my Forge. Not too many Beta Users in Wisconsin. 
If you could find thinner bolts/whatever to use, I think you could. Hard to
say without trying it.
Outside of analog watches, the widest selection of small hardware I’ve encountered is in the model train industry. Tiny taps & dies, but of course that involves making the hardware you need.
The OD of a 0-80 screw is .06"
They are tiny!
https://www.amazon.com/dp/B00917B8BS/ref=biss_dp_t_asn
https://www.amazon.com/Stainless-Small-Pattern-Machine-Finish/dp/B009EEZQBG/ref=sr_1_1?s=industrial&ie=UTF8&qid=1471977914&sr=1-1&keywords=0-80+nut
Could you use a living hinge in a flexible acrylic for a wristband? Or thin layers of HDPE? What would possible problems or weaknesses be?