Sure, you'll now say that A's PK field related to B's PK field has a UC, though that means that A's PK is in fact that field, and all other fields in A's PK aren't needed (as the field related to B's PK is the one which makes the row in A already unique)

Yes I could change the table design to this...

tbl_file
-------
FileID int pk
FileName varchar

tbl_player_skin_image_value
-------------------------------
FileID int pk fk
PlayerID int fk
ImageID int fk

...and I think this whole problem goes away.

Thanks.