Going by this schematic
http://i605.photobucket.com/albums/tt137/pinkjimiphoton/MagnavibeSchemsmall.jpg both of the potentiometers are being used a variable resistors, when you turn them all way in one direction lugs 1 and 3 are connected and the resistance is zero Ohms, turned the other way the resistance is the total resistance of the pot. Therefore if you use a 10k pot instead the maximum resistance is about half what the circuit wants.
The depth pot controls the maximum brightness of D1 which then controls the resistance of PH1, the higher the value of the depth pot the dimmer D1 will be, so using a 10k pot you won't get the full range of depth control. In this case the way the circuit responds will be different anyway depending on the exact components you use for D1 and PH1, so a 10k might be fine or a 25k might not be enough.
The speed pot is a bit different because it is in parallel with a 27k resistor, so if you know your Ohms law stuff, the total maximum resistance is about 12k, which is pretty close to 10k so if you remove the 27k resistor a 10k pot will work about the same.
https://en.wikipedia.org/wiki/Parallel_resistors#Ohm.27s_law.
You can change the value of pots but you can only make them smaller and change the taper, have a look here for more info
http://www.geofex.com/Article_Folders/potsecrets/potscret.htm
