>> Is there a way to changed the default RAW files associated to a bin file without reapplying the textures?
A bin file defines what textures it uses. For example, the stock bigfoot truck in the game uses BIGFOOT1.RAW and BIGFOOT2.RAW. So, if you want to repaint the bigfoot truck, you would paint the files, name them something unique (eg MYTRUCK1.RAW and MYTRUCK2.RAW) and you tell the bigfoot.bin to use your files instead of the originals. You would then rename BIGFOOT.BIN to whatever the name of your truck is (eg MYTRUCK.BIN).
Tip. Do not name your truck so it ends with a number. Or, at least, not the numbers 0, 1, or 2. (eg MYTRUCK1.BIN or MYTRUCK2.BIN) This confuses the game because it looks for low detail models using that number scheme. It'll work in ninety percent of cases but it's a good habit to avoid it so you don't run into the other ten percent.
>> The tutorial had Bigfoot's hood section
Looks like you're using bigdogge's mapping tutorial. If you have just repainted the stock files, you don't need to "remap". You can "replace" like I've described in answer to your first question (and malibu350 has as well). If, on the other hand, you have done all new textures, then yes you'll have to remap. Have you seen this page?
http://mtm2.com/~mtmg/repaint/
Best place to begin.