The fan is on the CPU side of the board - which is on the opposite side from what you can see and access - so there should be no issues with the HDD/SSHD cables on the other side.
Unless you want to (potentially) void your warranty and attempt to fix yourself, you might want to contact Intel Customer Support about a replacement unit.
I agree with N.Scott.Pearson, there should be no issue according to your description about that noise. Please contact Intel® Customer Support:
Just one more comment I thought was worth mentioning: In the latest generation, support for replaceable lids is included in the NUC designs (this allows for features like wireless charging, etc. to be added). It is thus not inconceivable that someone could impede the processor fan if they fiddle with the removable lid or what's under it. It doesn't sound like this is the case here, however...