1) Welcome to the forum.
2) Regarding the link you cited for the vendor in the Netherlands --
www.cmsnl.com/bmw-c-400-x-0c09-0c19-2019_model58775/battery-cover-blank_46638388899/ -- it shows up in my desktop browsers (Firefox, with a lot of security add-ons, and Safari, with no add-blockers, etc.) not as white, but just another needs-to-be-painted "Rohteil/Blank" piece (which, as you can see, they call BATTERY COVER BLANK).
Here's my screen grab of that page:
3) Doing a search for
bmw c400x battery cover alpine white, Google's AI response (which, like all AI responses, may or may not be correct) asserts the following:
This really surprised me, but after some minutes researching Beemer parts places seems to be the case.
I mean, not only did I look for your Alpine White cover (with or without that U751 paint code -- see, for instance,
www.bike-parts-bmw.com/bmw-motorcycle/C%20400/2018/C_400_X_-0C09_0C19_/Body-equipment/Trimpanel-components-U751-alpine-white-3/9/51_A132/51/607340C09) just revealed a boatload of those "Rohteil/Blank" parts.
And then I went looking for body parts for my "Callisto Gray Metallic" C 400 GT, at a typical parts fiche site, e.g.,
https://shop.maxbmw.com/fiche/partsfiche.aspx.
Some individual body parts that are actually painted in a bike's advertised color, such as the right or left "rear trim panel," show up as "Rohteil/Blank,," with no other info.
However, those same originally painted parts are also grouped together, for color purposes, e.g.:
But since they have
identical part numbers to the "Rohteil/Blank" parts, I'm left to surmise that those paint codes mean, "you want it, you buy it, you paint it yourself, using the paint that corresponds to those codes."
3) As I say, this surprises me. At different times, I owned two Burgman 650 scooters, for a total of 11 years, and so occasionally needed to buy some body parts.
Suzuki, however, offered those replacement parts painted from the factory, with each part that differed only in color having a different part number, e.g.:
I had
assumed that BMW bodywork replacement parts would work the same way, but now I think otherwise.
Perhaps someone who's actually purchased specifically colored bodywork parts for our scooters could chime in here, and settle the matter.
4) I've actually drilled a few holes through bodywork myself, in both my former '22 C 400 GT and in my current '23 C 400 GT. It just takes the best planning you can do, and nerves of steel. From my C 400 GT gallery:
https://billanddot.com/C400GT/#S-28,
https://billanddot.com/C400GT/#S-59, and
https://billanddot.com/C400GT/#S-137.
If you're worried, one possibility might be for you to buy the replacement battery cover, in its apparently stock gray color, for $65 or so. And then do the "first take" of your mod on that replacement part. Once you're satisfied that it came out okay, duplicate your work on your original white part, perhaps using your first-take-cover as a template.
That's all I got.
In any event, good luck on your quest, and on your mod.