Oh, why not, everything is possible.
You don't need Ya cash, Ya not a payment system, not Ya something-there-yet, and here it is: https://money.yandex.ru/quickpay/form
Everything happens so: sent GET request with the amount, wallet of recipient, method of payment (Bank. card, J. D), the amount ID of the order and other things. In the end, the user gets to the payment page card with a minimum of fields: card number, CVC, name, everything.
The user enters the card data, confirms 3DS second, the money immediately fell on the wallet of the seller, and the user will redirected on successURL specified in advance.
Any legal entities, individual entrepreneurs or paper contracts. There is no obtrusiveness on the part of Yandex, and he could, for example, instead of the payment card to force the user to have a wallet in me.d, to replenish and to pay. No, no nothing, even the account of the Yandex do not have to have the purchaser.
Here is the manual query parameters: https://money.yandex.ru/doc.xml?id=526991