Since the products from the old versus the new business are very different, it's unlikely that this strategy will be very effective. If you do email this list, I'd consider the following:

-send a personal text based email, not a fancy HTML marketing email
-thank them for their past purchase and let them know that you are starting a new business and would love their feedback/support
-give them a very easy way to opt out of future mailings.

Safest thing is probably to give them an opportunity to sign up for your new list. Glad to chat more about this email and other growth strategies.