Absolutely. All
carbon is good carbon. (Unless it's a oil spill washing up on your sea shore).
Mulch goes on top of the soil --- don't till it down into the soil profile. As long as it stays on top of the soil, it will not tie up nitrogen. With raised beds, it will be easy to rake the mulch layer back when you plant, and then put it back into place.
You'll find that the mulch will break down quickly as soil life increases. You'll be mulching and remulching a couple of times a year as the population of worms, bacteria and other biota grows within your soil.
If you want to jumpstart that mulch a bit, pile it up, wet it well (and add some
urine if you are so bold) turn it with a couple of big shovels of
compost and let it sit in a pile for a month or two. That will innoculate it with microbial life. If you've got access to
coffee grounds, mix those in as well, as it'll give some greens to your browns and some nitrogen to your carbon.
Walnut isn't the best choice for mulch, but other than that, the woods you've mentioned are great.