that sounds to me like someone has been handed several forks, chopsticks, knives etc. and is getting irritated. "Do you have ANY kind of spoon?" "Some kind of spoon" seems more neutral. my two cents.
While I agree with you about the tone, can this realistically mean the latter translation? What exactly fits the definition of "some kind of spoon" that isn't actually a spoon? (okay, a spork, but who has that)
Do you have some spoon, do you have any spoon - both are rejected. I must neseccarily use "kind", am I right?