Depending on the theme you're using, this code is usually in a file like sidebar.php in the theme folder. You can edit it directly there, with a little bit of HTML knowledge it's pretty easy to do.
See Using Themes in the docs: http://codex.wordpress.org/Using_Themes
If you have correct permission settings, you can edit the theme through the admin login -- click on Presentation then Theme Editor. Careful though -- once you update there's no undo.
When I do this, what I do is cut-and-paste the whole sidebar.php (if that's the right file for your theme) into a plain text file (you could use Notepad -- I prefer UltraEdit). Then, I do my edits within the browser, and if I make any mistakes, I can always restore from the version I have kept aside.
>> I still want people to be able to subscribe to my blog - I wont remove that through removing the links, right?
You're not removing files like your feed when you do this, just the link to it. It's only a link you're changing -- the feed links should still be in your
<head> code for the page, so the feeds are still there (to be recognised by Firefox etc) -- but I'm not an expert on Feeds so someone else may have better info on that for you!