Not real sure if your asking if there is a way to set a default signature, or if there is a way to make it assume that one of the signature options should always be enabled when you are updating a ticket.
If the former, you can open
/inclde/staff/ticket-view.inc.php
circa line 475 through 498
<tr>
<td width="160">
<label for="signature" class="left">Signature:</label>
</td>
<td width="765">
<?php
$info=$info?$info:$thisstaff->getDefaultSignatureType();
?>
<label><input type="radio" name="signature" value="none" checked="checked"> None</label>
<?php
if($thisstaff->getSignature()) {?>
<label><input type="radio" name="signature" value="mine"
<?php echo ($info=='mine')?'checked="checked"':''; ?>> My signature</label>
<?php
} ?>
<?php
if($dept && $dept->canAppendSignature()) { ?>
<label><input type="radio" name="signature" value="dept"
<?php echo ($info=='dept')?'checked="checked"':''; ?>>
Dept. Signature (<?php echo Format:($dept->getName()); ?>)</label>
<?php
} ?>
</td>
</tr>
you can change that code and make one of them default instead.