Important:
1. Use escrow
2. Beware of impersonators.
3. ALWAYS check everything. ie trade history, reputation, trust feedback, etc.
4. It would be better to trade with trusted/reputable long time users.
5. Again, do your own due diligence.
ID verification is not required (which is what you want), but do be careful of scams. There are plenty.
Frankly, I am hesitant to point you there as there plenty of scams, but, just use your common sense and you should be fine.
I'd recommend both zazarb : https://bitcointalksearch.org/topic/selling-buying-btc-preev-okpay-pm-payeerpp-escrow-service-1092531 and shdvb ; https://bitcointalksearch.org/topic/since-2014shdvbs-cryptocurrency-exchangeusdtbank-wirepayoneer-583572 but I'm not sure if they're currently taking skrill. You could send them a PM.
Otherwise, take a look at these list of exchanges : https://www.bestbitcoinexchange.io/ you could check which ones does not require ID verification.
If nothing works, then I hope you get cleared at Virwox. Or someone else can suggest others.
Does Skrill require ID verification?
It's really difficult if not impossible to find a way to buy bitcoins with skrill without providing ID. Is visiting an actual bitcoin ATM possible for you? Sounds like it might be a good option for you given the fact you're underage. I've spent a great deal of time trying to find ways to buy bitcoin with skrill and the few places I found, all of them required ID verification.