You’ll need to customize your Shopp template to do that. Under Shopp settings, in the Presentation tab, check “Enable theme templates”. That will copy the default Shopp template into your theme directory. Then from your theme directory you can edit the Shopp templates any way you like.
To get rid of the product quantity dropdown, look in product.php for this line and comment it out or delete it:
<?php shopp('product','quantity','class=selectall&input=menu'); ?>
Users will be limited to adding one item to the cart.