Yes, you can hand-write a check, but it still needs to follow guidelines specified by NACHA and ACH, which includes the 9-digit routing and account numbers. Anything else ist just an IOU.
which that 9 digit routing number can be found from 1000s of places online, calling the issuing bank or just asking when you go to your bank.
The bank could manually enter that check in with you giving them the routing number hand you the check back and you swallow it.
The routing number just must be known it does NOT need to be on the physical check to be cashed.