A prominent Spider-Man modder has worked on an experimental first-person mode for the game, showing off web-swinging from the (slightly nausea-inducing) perspective.
YouTube user jedijosh920 first released gameplay of the mod with a fixed camera perspective, meaning the first-person view is steady as Spider-Man swings around New York.
This version is probably more comfortable to use but does come with some caveats, as when the player performs tricks and flips in the air, the fixed perspective...