you don't need to hide links. If all you want is to prevent link juice from leaking you can add nofollow tags to your links. I think there are plugins that can do this automatically, but if not, you can do it by simply typing the tag manually when you create the link but if you have 100s or 1000s of links that you need to nofollow... well, it's going to take a while
Code:
<a href="https://whateverthelinkis.com/" rel="nofollow">whatever anchor text you want to use here</a>
But if you were actually inquiring about how to hide the affiliate links instead, now that's a different story and involves cloaking. The PrettyLinks plugin can cloak links, but there are probably other options, but PL is what I use, so that's what I can recommend.