Deleting a product won't remove orders for that product from your Transaction Log, as that is an unalterable permanent record of all orders we have processed for you; however, it will remove that item from the Product menu in your Transaction Log, which only lists your current products, so you won't be able to run a log search specifically for that product's sales alone.
If you want to make your affiliate program private, you can simply refrain from pasting your sign-up link code anywhere public; instead, just copy the href= URL (e.g. https://www.e-junkie.com/affiliates/?cl=XXXXXX&ev=XXXXXXXXXX) from your sign-up link code in Seller Admin > Affiliate Program Settings and email that link to approved affiliates personally.
Also, if you happen to have posted any product listings to your E-junkie Shop and our Marketplace (you haven't, so this is more for the benefit of anyone else reading along here), be sure to un-check "List affiliate program in E-junkie Marketplace", so those product listings will not show any affiliate program details.