The OEM size of your tire was either 195/70R14 or 195/65R15, depending on your trim level. V6’s got a 205/65R15 tire. These tires have diameters ranging from 24.7" to 25.5". Your “junkyard” spare has a diameter of 24.6", so it is slightly smaller than the smallest tire size available on 2002 Accords. [If anything, the outlier is your “owner’s manual” spare, which has a diameter of only 21.9".] Both tires are far narrower than any of the OEM choices. So I can’t see how the junkyard tire would have any clearance issues. If it fits in the spare tire well, put it in and stop worrying.