There is nothing shady about a site not saving your credit card info. It actually makes theft more difficult because if someone gets their hands on your account they will be unable to buy anything due to not having your credit card info.

Also you can use Paypal to buy Crysta, and Crysta can be exchanged for services like a name change, extra retainers or buying store outfits/mounts/etc. Crysta can be bought on the Mog Station.