The particular type of officer uniform the spy is wearing doesn't affect the behavior of other officers , right? The only difference in behavior is between soldier and officer uniforms?

Yes exactly. For more info on that you should refer to the game manual. You can only have effect with the disguised spy upon lower ranking officers. To have an effect on officer you have to get the higher type of uniform.

I might be wrong because it's been a while, but I thought that if you just stood next to an SS officer he could eventually figure you out regardless of what you are wearing.