Just for starters, you could seek clarification from your Bank on the application of a separation agreement other than to partners in a de facto or marital relationship. The Bank should be able to provide you with a pro forma agreement acceptable to them, as well as advice whether some type of separation agreement is necessary.
You could then go to a lawyer armed with all the factual documentation ( which might be a cost saving on the lawyer’s time).
I take it that you are buying out the other co-owner, by agreement or at their request. You should have documentation to this effect to provide to the lawyer and Bank.