The requirement is for the construct of the cap with an agency specific logo as well as the procurement of a specific number of caps. This is a two step process hence:
Can we as an agency use OM funds to purchase the item?
Can the GPC be used to fulfill the requirement?
It appears that based on the information provided that 1) you can use appropriated funds to procure command (organizational) ball caps as long as they are not considered part of the "seabag" and are considered organizational and the property of the organization. This is an excerpt from the Department of the Navy, Simplified Acquisition Procedures Guide:
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Uniform items that are part of the seabag are issued to Navy personnel upon enlistment and are to be replaced by the member with an annual cash allowance (Clothing Replacement Allowance). Therefore, seabag items will not be purchased with Operating Target (OPTAR) funds except as provided below. Organizational or personal protective clothing (aiguillettes, special safety shoes, disposable coveralls, etc.) is the property of the organization, remains with the organization and is paid for with OPTAR funds.
1. Seabag items can be issued or replaced as work clothing and procured using OPTAR funds for mess management specialists (e.g., tee shirts, trousers, caps, aprons) and for personnel whose work is of a destructive nature to clothing (e.g., cleaning fuel oil tanks, entering boilers, decontamination work).
2. Shoulder Sleeve Unit Identification Marks. Initial provision is free to each attached member and paid with OPTAR funds.
3. Name Tags and Patches for Flame Resistant Variant (FRV) Coveralls. Commands required to outfit sailors in FRV coveralls are authorized to purchase FRV fabric embroidered and/or embossed leather patches. Name tag and patches can be procured from authorized vendors that have been certified through the Navy Clothing and Textile Research Facility. For a list of the certified vendors and ordering procedures see Naval Message R131900ZFEB14ZYB. Naval Message R191900ZJAN17ZYB announced the approval of the Improved Flame Resistant Variant (IFRV) Coveralls and the transition from the FRV Coveralls to the IFRV Coveralls to occur in FY18. This message is available at http://www.public.navy.mil/bupers-npc/support/uniforms/Documents/COMUSFLTFORCOM%20R%20191900Z%20JAN%2017.pdf
United States Navy Uniform Regulations (NAVPERS 15665 (series))
31 USC 1301(a)
37 USC 415
This is further supported by NAVADMIN 200/14, which states:
2. Command ball caps are organizational clothing that may be purchased with appropriated funds and issued in accordance with NAVPERS 15665I (01JAN11), chapter 6, article 6801.
It is also highly recommended that you check with your local comptroller, as organizations can be more restrictive than any existing guidance and/or regulation.