Cable for MEMS Accelerometer
I've used single shielded RG178 with the NI 9234 in the past with good results.

The ADXL1001 has a single-ended output, and pseudo-differential acquisition usually has poor common mode rejection ratio. Twisting pairs is a tactic to turn EMI into common mode noise, but since you don't have a differential signal nor acquisition hardware with good common mode rejection, the best cable for you is a shielded coax.

Your goal of "(almost) no interference" may be difficult; there is only so much you can do with the physics of shielding to reduce noise in the signal.

You can try the various AC/DC coupling options on the 9234 and see if one of them is better. AC coupling dampens low frequencies. If 50Hz is not in your frequency range of interest, consider adding an analog or digital filter. Failing that, hopefully the "small peak" you describe is small enough compared to the signal you are interested in for it to be ignored.