Elias here with Shopify Support. That's a great question!
There are many third-party apps that can control product availability for deliveries, although it may be harder to find one that can set different delivery dates for certain products. I've looked through many delivery apps and, by reviewing their plans and features, I was able to find a couple of apps that can do this. However, it's important to note that setting different delivery dates on specific products is only available on a specific plan that they offer.
If you need any assistance with these apps, you can always reach out to the developers through the contact information found in the Support section of their app's page.
Please give these two apps a try and let me know if they're able to accomplish what you're looking for!