Hi,

Create a group for that list and give permission as "View" and then add this group to that list permissions. If not when you use security privileges the site will be open with admin account (where it have full control on site) so after this you need to add one or 2 lines of code so that the site will open by using current user name. And if he have view access he can just view and on click on doc also, he can download doc with his id only.
One thing is with out view access i think we can't give option to download docs.

I hope this will help you.