[Wolf20482]

According to Quora:

You can use Skrill without card or bank account but you will be able to use it only with other Skrill users. You will be able to top up your account from other Skrill account. You can get even a Skrill card and than use it. Skrill will be your payment account.

And for the Monero to Skrill exchange, to date, I only know this site https://exchanger24.org/xchange_XMR_to_SKRL/ (I've never tried it but I know about it). You just need to fill in the forms about how much you need to convert and enter your informations. I can't help you with this site since I've never tried it and I only send the site to you as a suggestion.
Good luck and tell me your opinion if it works/doesn't work!