As you are, effectively, not 'placing the device on the market' you may be able to import the product. This demands that you and your 'parent company' are part of the same economic entity.
It would also be a good idea to label the device very prominently (before shipping) along the lines of 'Caution: this medical device is not CE marked and must not be marketed or put into service'. See Article 4, paragraph 3 of the MDD.
I'm not sure if you mentioned Article 4, paragraph 3 only for the label, but in general it's not applicable to internal prototypes, only for medical devices (finished) that are shown. We can argue that these can include prototypes (who would know the difference?) but it's clearly not the intention of the paragraph.
Regarding the OP, unfortunately, there's no clear mention of prototypes in the directives, and manufacturers often thinks that prototypes do not need any oversight, which is not true. We may argue that initial prototypes (internal, not to be used in humans) will not comply with the regulations, but a prototype to be used in humans (usually near-finished or finished), which seems to be the case of the OP, you need to comply with the regulations, and as I mentioned, you need for it to be an investigational device.
As you need to comply with the regulation, this goes back to my previous comment, the device which does not have CE Marking (in the way to complying with the regulation, it may not have the mark itself, as Annex VII mentions) cannot be brought into Europe.
So you may not have to apply the CE Mark, but you have to comply with the CE Marking Directive. Maybe this makes things more clear.