The regulations require the construction contractor to "maintain a current file of the names, addresses and telephone numbers of each minority and female off-the-street applicant and minority and female referral from a union, a recruitment source or community orgnaization and of what action was taken with respect to each individual. If such individual was sent to the union hiring hall for referral and was not referred back to the Contractor by the union or, if referred, not employed by the Contractor, this shall be documented in the file with the reason therefor, along with any additional actions the Contractor may have taken." 41 CFR 60-4.3(7)(c). I interpret this regulation to permit you to refer this person, who walks in off the street, to the applicable union, but you still have an obligation to keep your own records of who you referred over to the union. Having an "off the street" applicant log that collects address and phone number, too, would meet the requirement to "maintain a current file of the name, address and telephone number." I would encourage you to maintain the log for men and nonminorities, too. Finally, the construction regulations were written (and not updated) since before the disability self-id requirements came into effect. I would encourage you to solicit race, gender, veteran status and disability status of these applicants, where possible. As you appear to note, the disability form is the official OMB-sanctioned form, CC-305, "An Invitation to Self-Identify."
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.