I don't think any part has the right to represent the whole country - but the records should be treated separately in my opinion. When East Germany and West Germany entered World Cup qualifying, they were competing against each other - even if the people both felt they were representing Germany.
Also, it was easier to get selected for East Germany than it was for West Germany (less people in East Germany) and therefore a cap for East Germany is not equivalent to a cap for West Germany (also, there is the issue that West Germany were a stronger national team). So, someone who has played 20 times for East Germany may not even have been selected once for a united Germany. Therefore, how can we say that someone who played 20 times for West Germany and someone who played 20 times for East Germany are somehow equivalent in achievement?
Whether or not the people wanted to be separate is not really relevant. The teams played under the restrictive rules in force at the time - i.e. - players from the East played for DDR, and those from the West played for FRG. The teams played as 2 separate national teams. Just as, for example, Hong Kong and Macao continue to play separately from China, there would be no question of their results being included in the China total - even though the people themselves might feel Chinese, they compete against China in the Asian Cup and World Cup.
Also, England, Scotland, Wales and Northern Ireland are independent in terms of football. But if one day they lost this footballing independence, it would be strange to include all players' caps together, as at the time they were playing, they were not playing for a United Kingdom team, because it did not exist. Similarly, the FRG and DDR players were not playing for a Germany team, because at that point in time, politically, it did not exist.