Is the there a proper way to present a contractor with a letter of appreciation base on the guidance provides? Or is there a proper method that has been vetted by a legal office or contracting officer that provides precedents for this action?
Per FAR 3.1.1-1 - Government business shall be conducted in a manner above reproach and, except as authorized by statute or regulation, with complete impartiality and with preferential treatment for none. Transactions relating to the expenditure of public funds require the highest degree of public trust and an impeccable standard of conduct. The general rule is to avoid strictly any conflict of interest or even the appearance of a conflict of interest in Government-contractor relationships. While many Federal laws and regulations place restrictions on the actions of Government personnel, their official conduct must, in addition, be such that they would have no reluctance to make a full public disclosure of their actions.
Since you are AF, you should seek additional guidance from the USAF Guide for the Government - Contractor Relationship in the section on 'Guidelines - Recognition and Awards', your Contracting Officer, and the cognizant Legal office representative. The contracting officer should be the only one communicating with the contractor with issues of either good or bad performance of contractor employees.