If it were me... and there was 'no way' to get the unique customer ids from anywhere else as part of the web service I would do the following...
Create the Order table as it is.
Then scan the Order table and build a unique customer table.
Actually that's what
@stevel05 recommended.
You have to do the first part anyway, the second part is an extra process but a really small one.
How many records are we talking about?
Can you not interrogate the web service to give you just unique customer ids or something? I guess this is outside of your control?