I don't want to focus on creating the shape outline as Catija's answer is a very simple approach for something like this. If this was a little bit different then other options might be viable as well. Perhaps using Plasticine or silicone to create a mold of the void. It would allow you to trace around the mold you create and get a gauge on depth. Unless you plan on repeating this those options are not very efficient.
Cutting the veneer
When creating the veneer you have a couple of options. You could cut out the shape from an existing veneer piece or cut your shape from larger stock and slice the veneer off of that. If you are just cutting preexisting veneer a craft knife might be enough. Warning if you go that route to not attempt to cut all way though at once. The knife could catch and follow the grain potentially ruining the cut.
A bandsaw would be a well rounded tool in either case. Using a fine tooth it will make easy work of the template and reduce the amount of sanding potentially required. Beware of the kerf when cutting your veneer. Cut outside the line you made.
Make your own veneer
If you don't have veneer or the veneer you have does not fit inside the void perfectly then you might have better luck cutting your own veneer (too large is fixable by sanding but too small is harder to recover from.). Use stock large enough so that you can maneuver around the bandsaw with your hand comfortably away from the blade. First, bring the fence ~0.5mm from the blade and push through. Consider making it a little thicker and sanding the face because I cannot tell from the photo if the wood is perfectly flat or contoured. With your new perfectly size veneer you can now cut it to shape.
Help prevent sanding an sizing
If you want to get cleaner cuts on your veneer when using power tools like the bandsaw you can always sandwich the veneer inside some sacrificial wood. This will reduce the tear-out on the veneer to nothing.
Pay attention to the direction of wood grain
One major point about cutting your veneer is make sure the length of the shape you are making follows the grain of the wood. If you cut it against the grain is will weaken the wood making it easier to break in half. Notice the grain direction in one of the other partitions of the bracelet. You should cut the veneer the same. While it might be fine once set you will notice a difference if you are sanding it or maneuvering the veneer.
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