Lol, well after pounding away at this for the past hour, I figured it out as soon as I posted the question!
The answer was to move the $hellishsimplicity_colour = get_option('hellishsimplicity_colour'); to above my IF statement.
PHP Code:
function hellishsimplicity_head() {
$hellishsimplicity_colour = get_option('hellishsimplicity_colour');
if ($hellishsimplicity_colour == "blue") {echo "<link rel="stylesheet" type="text/css" href="' , bloginfo('template_directory') , '/styleblue'.css" />";}
else {echo "<link rel="stylesheet" type="text/css" href="' , bloginfo('template_directory') , '/stylered'.css" />";}
}