There is absolutely no need to let wood chips sit before using them as a mulch. The "nitrogen-robbing" you refer to does happen, but it happens only at the soil-mulch interface and not below the soil surface, where the plant roots are. Here's some info to back up my statement. As the chips decay, the bacteria that "robbed" the N die, releasing it back into the soil. At that point, the cycle is self-repeating, so you won't need to add any amendments after that unless you feel the need to.
You especially have nothing to worry about since the chips are being used for paths. If it matters, I've been using chips for over 15 years now, in ornamental gardens, and have absolutely never had any issues. And my soil is great :)
I'm more concerned about your desire to use cardboard in your garden beds. This is actually a terrible idea - the science behind this is quite clear. First, here's some information from about 10 years ago for reference. The author is Linda Chalker-Scott, a professor emerita from Washington State University and a respected biologist.
Now, for more modern information. This is from a blog maintained by the horticulture professors at the same university. Here's the relevant post. To pull a little bit of this information into this answer, one of the biggest issues with cardboard is its ability to reduce oxygen movement into the soil, it also can cause issues with water and insects; this is noted in both references I've included. Be sure to read the comments section, as Dr. Chalker-Scott addresses Charles Dowding, a proponent of using cardboard, in her comments.
You can easily go no-dig without cardboard. Here's my method for my vegetable garden. This is anecdotal! But it has worked for decades for me (Zone 5, USA - min temp in winter is about -15F to -20F).
For plants (rather than direct seeding):
- If desired, fertilize the soil.
- Plant the crop - tomatoes, cucurbits, whatever.
- Water the new plants.
- Put down an organic mulch (note that I don't use wood chips in my vegetable garden). For a mulch, I use cocoa bean hulls because they're relatively inexpensive in my area. Other options would be rice hulls, weed-free straw, shredded leaves, shredded newspaper (ONLY use shredded paper!)
For direct-seeded plants like carrots, beets, etc., I don't mulch until the seeds are up and have put out their second set of leaves. I then mulch much heavier between the rows than up against the seedlings, using the same mulch as above.
So - that's all there is to it. I never turn my soil over. If you use compost, then you can work it into the soil a bit if you want when you apply it, but other than that you should never need to dig anything with this method.
Will you get weeds? Sure, a few, especially around the edges of the bed where the mulch may be a bit thin, but after a couple of years of building tilth through composting and mulching, the weeds are a breeze to pull out.
