I found a deal on a Kindle with special offers that I want to send to someone for a gift. I don't have access to their Amazon account. Can I send them something like a voucher to remove (or just outright remove) the special offers for that Kindle for their account, without having access to their account? Is there some other way to remove the offers from the device without having access to their account? It's a Kindle Voyage, if it matters.
No. To remove the special offer, you have to login to Amazon and chat with its support.
Change the account owner to your friend. I don't have my kindle around, but you can find this option by navigating through the buttons in kindle.
Ask them to negotiate with Amazon. They are supposed to take away the special offer for free. They did try to charge, but backed off after I insist.