Hey there mate! Yes, you can afaik. Another user made the same query in the this board! And this is what NotATether suggested earlier in that thread. You should give it a try and I believe it would fix that problem of yours with Bitcore core and the internet! Quoting it here again for better visibility, in case u missed it! Hope that helps!
If I install Windows 10 on my PC, do I have to download the entire Bitcoin Core again?
Or if I want, can I backup my Bitcoin Core files to another drive and restore them later?
You can backup your datadir to an external drive so that when you reinstall Windows 10, you can simply reinstall the Bitcoin Core program and copy the datadir back to your internal drive.
Since your node is pruned, it should even fit inside a USB stick, so I don't think you will have to go out and buy any additional hardware.