If the HTML code for your Affiliate link looks like this:
<a href="https://www.e-junkie.com/ecom/gb.php?cl=XXXXX&c=ib&aff=YYYYY" target="ejejcsingle">Click here to view more details</a>
...then the URL portion of that (which you can provide to TinyURL.com or paste into a plain-text email or a browser address bar) would be just this part:
The X and Y parts in these examples would, of course, be different for you, and unique to your own particular codes/URLs. Then you could provide your link URL to a forwarding shortener like tinyurl.com or bit.ly etc.