Who handles the paperwork and filing of owner financing? i.e. lawyer, broker,
Both. You didn't mention if you are executing a Lease with the Option to buy (also know as a Lease-Option) or a Real Estate Contract (also known as Contract for Deed or Land Contract in some states). Would you perform your own open-heart surgery? If the Broker is using official NAR (National Associtation of Realtor) forms you should be fine as long as there is clarity as to what the terms are and what the conditions are that need to met to satisfy the terms. A contract is an exchange of goods or services. If this happens, then this happens, so to speak.
It is still best to hire legal counsel to draw the necessary paperwork needed for this transaction. Hire an experienced real estate attorney. Get a recommendation from a CPA, an attorney you may know, or find a reputable real estate agent to recommend you a RE attorney. Splitting attorney cost makes the most sense.