Disbursements to Beneficiary of Trust

I need to send periodic disbursements (weekly) to the beneficiary of a trust for which I am the trustee. So the paying account is the trust’s account, and the receiving account is in the name of the beneficiary.

The beneficiary does not have access to Zelle currently (or similar P2P systems). I am not comfortable sending the payment via BillPay because the sending account number/routing number would be displayed.

Are my only remaining options cash/check through the mail? Interested in low-admin ways to get this accomplished.

Another solution would be to transfer the money directly to the beneficiary’s bank.
Or…
If the trust’s bank wont send a bank check w/o the trust’s account info, you’re the trustee, change banks.