The "downside" is that any you find will probably have some degree of pock-marks from the seat belt contacting it. The one on my '66 Chrysler Newport is that way, too. Just part of the territory, I suspect. That part probably saw few replacement sales, so finding an NOS item might be somewhat difficult. Especially as by the time anybody might have desired one from Chrysler, they were probably already NS1 at that time. Not something the basic vehicle warranty would have covered due to "normal wear and tear" issues, I suspect.
As for the part number, in parts Group 23, in the illustrations for the seat upholstery and trim, they are Item "M". Which is parts group 23-108-98 Shield, Front Seat Side or Back. The particular illustrations I was looking at were in the '67 Chrysler parts book, but the parts group should be the same for '66, I suspect. CE/CL/CM 4dr sedan, 4dr ht, and station wagon are the same part for the solid bench seat. 2drs, bucket seats, and convertibles are different, as are New Yorker "CH" items. Bench LH Manual Adj 2767743, Lh Pwr Adj 2767745 SAME as '66 DH station wagon front bench seat.
Chrysler, Dodge, and Plymouth have their respective trim illustrations, so the same parts group but in different car line lists. Page IT-196 in the '66 Chrysler parts book. Page IT-248 for Chrysler listings in the '67 Chrysler parts book. Page IT-77 in the '66 Chrysler parts book for Plymouth Fury models. Not sure about '65 or '68, but suspect they are all the same as the '66 and '67 models.
Only '66 & '67 DH and PH models had the side shields, none listed for lower model bench seats, which were only vinyl with no side shields (per the illustrations).
Hope this might help with choices or other C-body cars for parts sources.
CBODY67