There's no problem from the standpoint of the maximum ratings to swap a 12AU7 for a 12AX7. But I've yet to see a phono-preamp circuit where this swap won't have a significant effect on the RIAA accuracy. If the circuit uses passive EQ, the 12AU7's lower plate resistance will affect the drive impedance to the EQ network, and alter its response. If the stage uses active (feedback) EQ, then the tube's lower transconductance will affect the loop gain . . . and the response of the active filter.
If you enjoy swapping tubes around, then certainly go ahead and give it a try - you won't hurt anything. But it's a safe bet that the sonic differences you'll hear are overwhelmingly caused by differences in frequency response, in the same manner as a tone control.