my only concern of switching the 1k to a 5k or 10 is if it will affect any voltage or other circuitry in the game ...
If the pot is a typical 3-wire setup, it is acting as a voltage divider.
- Operating voltage (usually 5v) and ground will be on the outer tabs 1 and 3.
- The pot output voltage will be on the center tab 2.
The difference between 1/5/10k pots is how much current they will draw.
- You can calculate this using Ohm's Law -- Voltage = Current * Resistance
- Equation rearranged to solve for current -- Voltage / Resistance = Current
- 1k draws 5mA -- 5v / 1kohm = 5mA
- 5k draws 1mA -- 5v / 5kohm = 1mA
- 10k draws 0.5mA -- 5v / 10kohm = 0.5mA
That's not a huge difference for typical electronic circuits, so as long as the Analog to Digital Converter circuit can operate with the lower current level, a 5k or 10k pot will be OK.

The greater concern when swapping pots is the difference in the range of voltages from a linear 60 degree pot compared to a linear 270 degree pot, for example.
- 60 degrees of motion on a 60 degree pot gives a full 5v range.
- 60 degrees of motion on a 270 degree pot gives a much more limited 1.11v range. 60/270 * 5v = 1.11v
Scott