In this challenge, I avoid using web-swings and web-zips, as well as not doing Hulk-jumps while playing as Venom; Also, I decided not to use the swing cancel exploit. While I technically don't swing, this exploit makes moving around easier and allows me to cheese difficult sections.
Got a few requests to do this. I didn't get the appeal at first, found this challenge to be pointless, but I changed my mind after giving it a try.
The chase sequences become a huge challenge without swinging. I couldn't just follow the target where they're going, I'm not fast enough to keep with them.
I came up with routes that allowed me to barely keep up with them, which invlove shortcuts and utilizing the rubberbanding mechanic (the farer you are from the target - the slower they move).
Beetle 1 and Goblin were the hardest chases to route with Electro being not too far behind. The remaining chases were pretty straightforward, even without swinging.
Also, I was able to beat 2/5 races with ultimate mdeal, and the remaining 3 with gold medal.
I think swingless is more interesting for Spider-Man 2 than in this game, but it had to be done sometime I guess.