I can't find my Worms 2 disk anymore, although I did purchase it. Can I download Worms 2 from the internet, or do I really need to find my disk?

No, you cannot download W2 from the internet (at least not for free)*. However, you can buy W2 again for next to nothing in a box set with Worms Armageddon from Team17's online store: https://secure.team17.com/browse.html?area=detail&skuid=79
The store ships internationally.

* Well you probably could but its a breach of forum rules to mention anything like that here, since Team17 take a dim view on piracy of their own games, for obvious reasons!