Don't have a tested solution herre but you could maybe use $link_category for this.
The link_summary.tpl begins like this
Code:
<div class="news-summary" id="xnews-{$link_shakebox_index}"
{if $link_shakebox_currentuser_reports gt 0}
style="opacity:0.3;filter:alpha(opacity = 30)"
{/if}
>
Excluding stories from main page could maybe work if you modify those lines to look something like this
Code:
<div class="news-summary" id="xnews-{$link_shakebox_index}"
{if $category_href neq "" &&& $link_category eq "category name here"}
style="display: none;"
{/if}
{if $link_shakebox_currentuser_reports gt 0}
style="opacity:0.3;filter:alpha(opacity = 30)"
{/if}
>
As I said this is not tested. If someone tries something like this please report here if it works or not.