Ok so this what I'm doing and it works like a charm.
Get a new short domain, that looks like you have your own private URL shortening service. I got some .cc domains
Let's say you get mack.cc
Now on mack.cc install:
Then upload an excel file with all the redirections following the instruction you'll find on the plugin site or somewhere else.
mack.cc/1 ---redirects to--> affiliate link 1
mack.cc/2 -----> affiliate link 2
Upload a robots.txt to block the entire mack.cc website from being indexed.
On mack.cc, on the redirection plugin setting you'll find statistics telling you how many times your redirect links have been clicked.
Plus on your website if you're using Jetpack stats all your mack.cc clicks will be tracked as external clicks and you can easily check how many times they have been clicked.
All your redirection are on mack.cc, so that lightens up your main site. All you have to do is to nofollow your mack.cc links on your main site because you don't want to send "link juice" to an empty noindexed site.
Hope that helps.