What value of exit pressure should I use in the design equations for a small liquid rocket engine nozzle for 200km-500km operating conditions? Since using zero as a value is not possible or else nozzle size will be infinite what is the exit pressure that I should use for my nozzle and how do propulsion engineers do it? I guess engineers use a rather low altitude value and let the nozzle be under-expanded at vacuum conditions. I have checked out these atmospheric properties tableslink for the tables but using those values gives a huge nozzle which is impossible to design and use. So please help me find a value that I can use.
Your goal is to design the best possible engine. Only you can define “best”.
The exit pressure is a parameter of that design: you can pick the value you use.
A priori, there’s no way to know which value to use to get that best design, because it enters in multiple ways: cost, weight, thrust, fit, etc. So you need to use multiple values to home in on the one you choose to use in your design.