I work quite a lot with American Cherry, and you absolutely need a strategy for dealing with the blotchiness. I find Cherry breaks down into two groups.
First is highly figured cherry, timber that has "curly" or "fiddleback" figure. I'll take some photos of this type of board when I'm in the workshop tomorrow. It's surprisingly common (in fact it must vie with Rippled Sycamore to be the most widely available, heavily figured timber that you can get with reasonable consistency in the UK). The test I apply is to look at a board from two completely different angles, if you get a holographic effect, where dark areas and light areas reverse when seen from different angles, then it's curly/figured, and you want a finishing routine that will
accentuate that figure. In my workshop that usually means an oil finish. Here's a chest from Doucette & Wolfe that's made from a particularly spectacular curly cherry and I'm pretty sure has a simple oiled finish.
Second is Cherry with normal figure, again the test is to view the board from two completely different angles, if a dark patch remains dark in
both views then the finishing challenge becomes how to minimise blotchiness. You've basically three choices. A coloured gel finish, which can be sealed with shellac if you want to add clear coats on top. That's a popular solution in the US, it works well enough, but to my eye it tends to deaden the timber and looks a bit artificial. Alternatively you can sand to far finer grits than you would normally use, out to 800 grit or even finer. You'll be surprised how effective this can be in reducing blotching. Finally you can finish with a clear coat, water bourne poly or whatever you prefer, and just let the timber age naturally. Cherry acquires an age patination incredibly quickly, in fact I have a real headache storing cherry because if one board overlaps another, even in my shaded wood shed, it will inevitably get a "bikini line"! Many makers take advantage of this "quick tanning" characteristic and leave cherry furniture outdoors to "sunbathe" for a couple of days. It may sound potty but I can assure you that it works. And once cherry has darkened like this any blotchiness then becomes much reduced, after a few years in a home it's almost invisible.
One final point, you say you're working with cherry veneer. If it's normal, commercial veneer (as opposed to saw cut veneer) then it's unlikely to be more than 0.6mm thick. So aggressive sanding is something to be avoided. Incidentally if you fancy working with curly cherry veneer you can easily source that too. I buy most of my commercial veneers from Capital Crispin, and they normally have curly cherry leaves available that are every bit as impressive as the Doucette & Wolfe example,
https://www.capitalcrispin.com/products.php
Good luck!