I don't really care where he'd be shooting them from, I'm just saying for a guy whose powers are all about being a spider, I would think the web production would be part of the package deal. I know the non-organic webshooters have been used as a plot device on many occasion (Whoops! Ran out! Lawl!) but it always struck me as wrong.Going by that same reasoning, he would be shooting web out of his ass. I just like the techno shooters because of fitting in with the comic universe origin.
I did see this on wiki
One biologist on the History Channel’s Spider-Man Tech suggested that it would be more plausible for Spider-Man to shoot webbing from the Submandibular gland beneath the tongue instead of from his forearms