Can the no cost contract be awarded by our Small Purchase Branch (which follows SAP) or would the contract need to be awarded by our major contracts division (awards greater than $250,000)?
This response is based on the information provided. We suggest you discuss with your contracting and legal department as appropriate.
Who awards the effort is a call you can make. A more important question is, "Why is a contract being written?". What you are doing (as described in your background information) is creating an agreement for use of space. This arrangement is much better codified through a Memorandum of Understanding or Memorandum of Agreement.
It is not clear what NRL receives in the contractual arrangement that would make it a binding agreement. Without consideration, there is no contract.
But again, there are no hard and fast rules as to which unit should/must execute the document, it is a local decision.