One thing you could try is downloading the papers before the user requests them so that they will be ready instantly for a user's request.

Example: User opens paper on page 1. Page 1 has citations to 3 other papers. Your tool instantly begins downloading the other 3 papers. User goes on to Page 2 which cites 1 other paper. You begin downloading the new paper. User clicks on the citation and your tool now has the linked paper already downloaded and ready to open.

Might be a bit of an imposition on sci-hub though.