Affiliate Link Concealment on Blog

I have a wordpress Blog, The primary goal is to keep the target URL hidden from visitors.

when visitor click a affiliate link on my wordpress Blog,

TARGET URL should be opened onmy own wordpress URL itself wihtout showing visitor my actual TARGET URL.

example .

my website : www.mywebsite.com

Affiliate target URL : www.targeturl.com

I have set up www.mywebsite.com/go/taget redirect to www.targeturl.com

but here user can see the URL "www.targeturl.com"

I want a way where when user click "www.mywebsite.com/go/taget"

it sould open www.targeturl.com homepage but on brower address bar , visitor can see something "www.mywebsite.com/tagethome" (hiding the URL www.targeturl.com)

hope you undesrtood my requirent fully .