Hi sandiknowles,
Thank you for the purchase.

Something like this is possible only with the CSS. You can add this CSS directly on the page between <style></style> tags or in Custom CSS field on wpDataTables settings page.

To hide New button add:

.DTTT_button_new {
    display: none !important;
}

To hide Delete button add:

.DTTT_button_delete {
    display: none !important;
}