You can probably just edit out the td class names (prev_strip, next_strip) and insert your code ... <a id="filmstrip_prev" rel="nofollow" style="cursor: pointer;">Previous</a>.
This might break the links, untested.
Section to edit or add in your custom theme.php
/******************************************************************************
** Section <<<$template_film_strip>>> - START
******************************************************************************/
// HTML template for filmstrip display
$template_film_strip = <<<EOT
<tr>
<td valign="top" class="filmstrip_background" style="background-image: url({TILE1});"><img src="{TILE1}" alt="" border="0" /></td>
</tr>
<tr>
<td valign="bottom" class="thumbnails filmstrip_background" align="center" style="{THUMB_TD_STYLE}">
<table width="100%" cellspacing="0" cellpadding="3" border="0">
<tr>
<td width="50%" class="prev_strip"></td>
<td valign="bottom" style="{THUMB_TD_STYLE}">
<div id="film" style="{SET_WIDTH}"><table class="tape" ><tr>{THUMB_STRIP}</tr></table></div>
</td>
<td width="50%" align="right" class="next_strip"></td>
</tr>
</table>
</td>
</tr>
<tr>
<td valign="top" class="filmstrip_background" style="background-image: url({TILE2});"><img src="{TILE2}" alt="" border="0" /></td>
</tr>
<!-- BEGIN thumb_cell -->
<td class="thumb" >
<a href="{LINK_TGT}" class="thumbLink" style="{ONE_WIDTH}">{THUMB}</a>
</td>
<!-- END thumb_cell -->
<!-- BEGIN empty_cell -->
<td valign="top" align="center" > </td>
<!-- END empty_cell -->
EOT;
/******************************************************************************
** Section <<<$template_film_strip>>> - END
******************************************************************************/