If you want to be able to actually craft with your main character, then, yes, you would need to spend skill points in blacksmithing and woodworking on your main. Skill-points are not shared by characters, so your main can never make use of what an alt knows.

If you want to just your craft everything while playing your alt, you can leave crafted items for your main to pick up in your bank. In this case you would not need to put any skill-points into crafting on your main.

Just keep in mind...You will have to play your alt in order to get all of the skill points needed to craft at higher levels.

For a good overview of all that crafting entails see the post here: forums.elderscrollsonline.com/en/discussion/194149/making-a-crafter-character#latest by @Ranique