Hi,
You should definitely use custom CSS. You can surely override them, just have to create higher specificity rules.
The problem with disabling them is, that the plugin generates all of the search bar CSS in one request, and they are not separated like that. So you either disable all of the CSS or none of it.
There is a simple programmatical way of disabling all of the CSS. Theoretically, you could collect all the required CSS from the plugin enqueued CSS files, then put them into a custom css file, along with your styles, then disable them via the above mentioned method. That would actually work.
There are usually 2 CSS files enqueued:
wp-content/uploads/asp_upload/style.basic-{OPTIONAL_QR_STRING}.css
wp-content/uploads/asp_upload/style.instances-{OPTIONAL_QR_STRING}.cssThe search results CSS rules usually either start with:
#ajaxsearchprores...
..or
div.asp_r
..or
.asp_r