You can ask for a signed message or ask for an email with the the same email registered for skrill. You may fully verify your account through email and phone numberto make it easier. If you want to have a transaction through an exchanger then bitpanda may act as a good option but they do not display fees publically.
What amounts can I send without the phone verification; do they block
your account if you don't sooner or later verify after certain period?
Any other sites other than bitpanda?