Slice salmon into approximately 1-inch thick cubes. Set into a gallon-sized ziptop bag or a large resealable container.
In a small bowl, whisk together oil, lemon juice, oregano, parsley, dill, thyme, paprika, garlic, salt and pepper. Pour half of the marinade over the salmon. Toss thoroughly until each piece of fish is coated. Marinate 15 minutes at room temperature, or up to overnight in the fridge.
If using wooden skewers, soak in cool water as the salmon marinates. This prevents the wood from charring and turning into ash when exposed to the cooking heat.
When the salmon is ready, assemble the skewers. Alternate a piece of salmon with a round of zucchini or yellow squash. Repeat until each component is used up. You should get at least 6 skewers but possibly up to 8 depending on how much you like to crowd the skewers. I tend to leave a tiny bit of space, maybe 1/4 inch.
Preheat grill or grill pan to medium heat and rub grates with oil. Grill skewers about 15 minutes total, turning every 3-4 minutes. Baste the skewers with the reserved marinade until each side is nicely toasted and the salmon flakes easily when poked with a fork.
To make the chimichurri, combine all ingredients in the bowl of a food processor and blitz until relatively smooth. Chunks of herb may remain - that's okay! Feel free to add more oil if you want a more vinaigrette-like texture.
Serve skewers over plates of rice and drizzle with chimichurri.