Hello JLO.

Yeah, you can hide those buttons when you add this CSS in Custom CSS field on wpDataTables settings page or directly on the page between<style>Your code</style> tags:

.DTTT_button_delete {
display: none !important;
}
.DTTT_button_new {
display: none !important;
}

Also, I believe you may want to hide the "Apply and add new" button from the edit modal as well, so you'll need this also:

.wpdt-c #table_1_apply_edit_dialog {
display: none !important;
}

Best regards.