With the physical advanatges in Spidey's ploy and his morals gone, he could overcome Wolvie physically with ease, pin those arms of his to his sides with webbing, and would (with one punch) KO Wolvie (a healing factor cannot help you if you're susceptible to being KO'ed in the first place, and that's the case with ol' Logan).
I know this means next to nothing, but let's take a look at Marvel's "Abilities" section of both spidey and wolverine:
Spiderman:
Strength: 4
Speed: 3
Durability: 3
Fighting skills: 4
Wolverine:
Strength: 4
Speed: 2
Durability: 4
Fighting skills: 7
Now....Spiderman may be slightly faster than wolverine, but those 120 or so years of fighting mean something. They mean reflexes and use of own potential to the fullest. Think no one's tried pinning wolverine to the wall with a net before in those years? Now i'm not saying this wouldn't go to Spidey, but i'm saying it wouldn't be as easy as you think it is.
~wickerman~