I think it could be done quite easily, replicating existing codes. You will need to draw the button on your own though.
So, for example, take a look in templates/main_post_form.ht
ml and replicate the code from let's say the bold tag this way:
<a href="JavaScript:paste_strinL(selektion,3,'[s]','[/s]','')" onmouseover="window.status='{$l_bb_strike}'; return true" onmouseout="window.status=''; return true" onmousemove="pasteSel()"><img src="https://www.minibb.com/forums/img/button_strike.gif" style="width:22px;height:22px" alt="{$l_bb_strike}" title="{$l_bb_strike}" /></a>
Put and translate $l_bb_strike into your language pack (lang/eng.php probably).
Then modify bb_codes.php, replicating for the function enCodeBB:
$pattern[]="/\[[sS]\](.+?)\[\/[sS]\]/s";
$replacement[]='<del>\\1</del>';
and for the function deCodeBB:
$pattern[]="/<del>(.+?)<\/del>/is";
$replacement[]="[s]\\1[/s]";
Don't forget about the button, which should be placed under /img/button_strike.gif.
That would be all...