I know this question is old but this is my idea, I did something similar, not exactly the same.
Because you can't submit the form if you remove the required fields like Category or Title, you can put a hidden INPUT field with a random value, as long as it is not empty value. In your override file templates/YOUR TEMPLATE/html/com_k2/default/itemform.php instead of showing category selection:
<tr>
<td class="adminK2LeftCol">
<label><?php echo JText::_('K2_CATEGORY'); ?></label>
</td>
<td class="adminK2RightCol">
<?php echo $this->lists['categories']; ?>
</td>
</tr>
You use something like this
<input type="hidden" id="catid" name="catid" value="-1">
Yes naughty users can use Firebug to put their values in that INPUT, but you still can build a plugin and listen to onBeforeK2Save event then set your default value of category to your own value (0, 1 , 2 anything) before saving the content to database. By using this way, you can generate title for your K2 item too.
<?php
defined('_JEXEC') or die ;
JLoader::register('K2Plugin', JPATH_ADMINISTRATOR.'/components/com_k2/lib/k2plugin.php');
class plgK2MyExample extends K2Plugin
{
var $pluginName = 'myexample';
var $pluginNameHumanReadable = 'My Example K2 Plugin';
function onBeforeK2Save(&$item, $isNew)
{
$item->catid = 10000;
$item->title = 'my own title';
}
}
Check the example plugin here: https://github.com/joomlaworks/example-k2-plugin (onBeforeK2Save is missing in the example plugin).
onBeforeK2Save is called in administrator/components/com_k2/models/item.php ("save" function).