Unfortunately, there is no way that I can think of to bypass that mission requirement. Additionally, as others have said the only way to upgrade your gear is to hunt the animals, and if you choose not to do that, you will be severely limiting yourself. In fact, I think it would be incredibly difficult to play through without upgrades because you will only be able to carry a single gun at a time and a pretty small cache of ammo for it at that.

Also, the island is packed (literally packed, to the point of being ridiculous) with 'aggressive' animals like Komodo Dragons, Tigers, Leopard, etc. that WILL ambush and kill you, frequently, especially if you aren't willing to kill them. 

The best advice I could give would be to maybe find a sibling or friend to play through those parts for you, then stock up on a TON of "Animal Repellent" syringes so you can use those when aggressive animals show up, but even then it's going to be tough... :(

• Minimum Level Requirement: 10. Enemies scale according to character's current story progress in playthrough 1, 2, and 2.5. Enemies scale up to a level of 69 (except for some defilers in the second playthrough reaching level 70).

http://borderlands.wikia.com/wiki/The_Zombie_Island_of_Dr._Ned

PS - just an FYI that site WILL contain spoilers so please be aware of that. I don't think that article has any really, but other places will if you go digging.

I've played through Uncharted 3 times as well.

That being said, it is a MUST rent, if not a purchase.

I've got GRID rented right now too - and I am confident I will be sick of it before the rental period ends.