Most parts (springs, triggers, sights, etc.), if under $100, do not require a permit or paperwork. Provided that the seller is a licensed exporter such as Brownells. If the part is over $100, or is something like a barrel, receiver, etc., then the export paperwork needs to be done. I ordered seveal parts to build my Marlin .45-70 the way I wanted it. Ordered in two or three separate orders, some needed paperwork and others didn't. The permits weren't hard to do, Brownell's was very easy and helpful along the way (they do this thing quite a bit), and I got everything I was looking for- oversize loop lever, XS Ghost Ring sights, Wild West Guns trigger, hammer spring, extractor, etc.
Stocks, as long as it's not the dreaded bullpup or some other heinous item, can be brought in if it's under $100 no worries. Boyd's and Stocky's have quite a few that fall into that category.