Don't do that, it will be disastrous for you.
Instead, send them a politely worded one-time announcement with an invitation to subscribe. Clearly mention that if they don't, this is the last mail they'll get from you, and keep that promise by deleting their address. You'll still get some pushback, but I think most people would find that acceptable.
> Instead, send them a politely worded one-time announcement with an invitation to subscribe.
NO. DO NOT DO THAT !
That is terrible advice and it is against the law.
Opt-in has to be done without inducement and of a person's own volition.
Sending a mail to someone saying "pretty please sign up" is not valid opt-in. It is spamming a bunch of people hoping they will opt-in. It does not matter if you got their mail another way (e.g. if they purchased a product, you can't then spam them trying to get them to opt-in for your mailing list).
One of the fundamental reasons the opt-in law exists is to stop people doing the shit you suggest and ensure that lists are correctly built in a clean manner.
At least with your suggestions there's some chance that their newsletter won't instantly get flagged as spam.
I'd do what you suggest, but send the newsletter from an separate domain once subscriptions have been confirmed.