Ok, here's an approximation. Taking all songs represented in Bronson (I still had the file handy from doing up Bronson for the Ballad Index so this wasn't that hard.) Keeping in mind that many of these tunes may never have been recorded on sound media and some may be so defective as to not be singable ("Willie's Lady," for one) AND also that others may well have turned up since Bronson finished in 1972... Still & all, I count 96 ballads with no trad. tunes. That leaves (uh......) 209 possibilities.

Since you were going to ask, these are the un-tuned ballads:
8, 15, 21, 23, 28, 29, 30, 35, 36, 48, 50, 59, 60, 70, 71, 80, 82, 87, 91, 104, 107, 108, 109, 111, 115, 118, 119, 122, 127, 128, 130, 133, 135, 136, 137, 138, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 158, 159, 160, 165, 166, 168, 171, 172, 174, 175, 176, 177, 179, 180, 184, 189, 190, 194, 197, 198, 205, 207, 220, 224, 230, 234, 242, 244, 249, 259, 261, 262, 263, 264, 268, 271, 290, 291, 292, 294, 296, 297, 300, 301, 302, 303, 304, 305