I am not licensed in your area, so my response is not intended to be legal advise but providing general information.
Ordinarily, courts can not award of attorneys fees in the absence of a statute or written contract. You had a verbal agreement. Examples of statutes that typically provide for attorney's fees involve family law cases, bad checks, landlord tenant, unpaid wages. Ordinarily, there is no entitlement to have fees on a bad debt.
My thought process is that you are going to be "out" the attorney's fee regardless. If the attorney writes a letter and you get paid, are you really going to want to go to court for the fee?
And, why pay money for a demand letter that the ex-friend can simply ignore? The amount of money involved is not large--compared to other law suits. It may be a lot of money for you. If that is the case, then you should prioritize your use of the funds. Instead of paying a lawyer for a letter, use the funds to pay the filing fee and get the case into court. No chance for the debtor to stall, delay or ignore. If they ignore the law suit you get a judgment against them. AND, Court costs such as filing fees and service of process fees are almost ALWAYS awarded by the Court. You are also entitled to ask for pre-judgment interest.
So, if you have $X to spend, go straight into the Court system and get ball rolling.
There is another approach, though. Collection attorneys typically work on a contingency fee basis. Unfortunately, the amount of your claim is so small that few will want to work on a 25% or even 1/3 basis. Perhaps I am wrong, but by sending the letter, the lawyer will be taking on professional responsibility and professional liability.
One warning, though. A final judgment is not like a child support or alimony award. It is a legal document whereby the debt is established as a matter of law, and then you have to go about the business of collecting on the judgment. Often, this means your coming up with more money to pay for a garnishment, or a levy.
SOMETIMES the best advise a lawyer can give is for the client to take NO action. Not spending good money chasing bad. This may bee one of those times. I do not know the filing fee or other charges you will have to pay.....but in my area it would be about $200.00. And when you consider the other costs......there is a scene in the movie "A Bronx Tale" where the character played by Robert Deniro tells his son, about someone who owes the son $20.00, that it might be the best $20 the son spent, as it keeps the borrower away from the son in the future. MAYBE this is a similar circumstance--you found out that your friend is not a friend, and thank goodness it was $600.00 and not $6,000.00.
Again, this may not be the legal advise you were looking for, but it may give you a perspective you had not already considered.
Whatever you decide, good luck.