0.15mv is about 8.5 db less than 0.4mv. If you are presently using the volume control on your preamp in the upper third, or perhaps the upper half, of its range, my very rough ballpark guess would be that 8.5db corresponds to around 60 or 70 degrees or so of rotation on the control.
Therefore, with no music playing rotate the control to a point that is about 70 degrees of rotation higher than the highest setting you presently use it at. See if the noise level becomes unacceptable at that setting, or if you run out of range on the volume control.
It would be prudent to allow some margin beyond that point, to accommodate possible inaccuracies in the specs, inconsistencies in how they are defined, and the fact that the amount of rotation is just a very rough guess.
If you normally use the volume control at or below the mid-point of its range with your present cartridge, then the 8.5db would correspond to significantly less rotation than that 60 or 70 degree estimate.
If an SPL meter is available to you, that would allow you to get a more precise idea of the calibration of your volume control, and eliminate most of the guesswork.