Oh, I found a way through walls.
291 frames faster than the current published run:
http://dehacked.2y.net/microstorage.php/info/438242934/32x-spiderman-web-of-fire-improvement.gmv
The trick does not save any time in these two levels, though:
http://dehacked.2y.net/microstorage.php/info/426326726/web-of-fire-level-skip1.gmv (About 2000 frames slower, even though the whole fiery factory level is "skipped" or dodged or something.)
http://dehacked.2y.net/microstorage.php/info/1025172347/web-of-fire-level-skip2.gmv (Final level is... circumnavigated? It is about 1300 frames slower.)
Recipe for the trick is here: Grab a wall, shoot web downwards, jump, shoot web again. Do this fast enough and you get inside the wall. You get easily trapped forever, but if the wall is narrow enough, it can be escaped.
The trick should allow some shortcuts in level 2, through the narrow steel walls, maybe saving ~10 seconds.
I don't like the web swinging, but I can try to help, if somebody wants to do a new run for this game.