10k ohm Potentiometer vs 10k ohm Resistor on LCD Display
No, it would not be correct to use a single resistor to replace a potentiometer.

On an LCD the potentiometer is used to adjust the bias level of the LCD - that is the contrast.  You need to use it to set a voltage between Vcc and Vee, which you feed into Vo.  That is, a voltage somewhere between +5V and -5V.

You can't do that with one resistor.

You can, however, do it with two resistors.  Some experimentation will provide the right values to use.  Pick a pair of resistors which add up to around 10K (the exact value doesn't matter that much) and join them together end to end.  The two ends are the equivalent to the ends of the track of the potentiometer, and the join in the middle is the wiper.

To change the "value" of the potentiometer you then need to change the value of both resistors.  If you reduce one resistor you need to increase the other so that they still add up to around the same value.  What you are working with here is not the actual values of the resistors, but the ratio of the values of the two resistors.