It is kind of hackish, but you could rename all the
emblem-symbolic-link.svg icons to something else like
emblem-symbolic-link.svg.bak respectively. Use
locate emblem-symbolic-link to find where they are.
But is there any reason you need to use a symlink?
Otherwise you could use a Launcher. Right-click on your desktop and select
Create Launcher..., and click on the
Browse... button and select your portable program.
Write a name for your Launcher and (optionally) select a different icon and your done.