This is an HTML/browser question more than it is a perl/CGI::Application question but I'll bite anyway. Each row would be its own form, have a hidden field specifying the runmode and the button is useful only to get the browser to submit the entry to the server.

<p><form method="POST" action="..."><input type="hidden" name="rm" val
+ue="foo"><input type="submit" value="Click here nice user"></form></p
+>
<p><form method="POST" action="..."><input type="hidden" name="rm" val
+ue="bar"><input type="submit" value="No, click *here* nice user"></fo
+rm></p>
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