Look in the file _main.php from the skin you made for something remotely similar to this :

<?php if( ! $Blog->get('force_skin') )
	{	// Skin switching is allowed for this blog: ?>
		<div class="bSideItem">
			<h3><?php echo T_('Choose skin') ?></h3>
			<ul>
				<?php // ------------------------------- START OF SKIN LIST -------------------------------
				for( skin_list_start(); skin_list_next(); ) { ?>
					<li><a href="<?php skin_change_url() ?>"><?php skin_list_iteminfo( 'name', 'htmlbody' ) ?></a></li>
				<?php } // ------------------------------ END OF SKIN LIST ------------------------------ ?>
			</ul>
		</div>
	<?php } ?>

Perhaps it is not exactly the same, but this piece of code need to go

Thanks so much for that. I had tried uninstalling the plugin "Categories Skin Tag This skin tag displays the list of available categories for the blog.", but those skin choices remained. I will now make the deletion you suggested and I think that will do what I need.

A lot has changed between the versions 0.9 and 1.8.6 and 1.9.2
But a lot of the skins are legacy and sometimes they still have legacy code in them.
That can be an explanation why it was not working by disabling the plugin

I followed your instructions and it worked perfectly to eliminate the skin choices for people viewing my blogs.

Thanks so much for your reply to me. I hope to learn this well enough (it's only my second day with it) to be able to return the favor to others eventually.