What I meant is that this sentence is incorrect because is the mix of two correct ones with different meaning:
1- "Chissà dove l'hanno/avranno messa!" (Who knows where they put it!) to mantain the English translation or 2- "Chi sa dove la abbiano messa?" (Does anybody know where they put it?) to mantain the form of the verb
Also I don't think that "chissà" and "chi sa" are interchangeable, at least not always:
1-"Chissà" is an interjection meaning "I wonder if/what/where..." "Chissà dov'è!" it's similar to a rhetorical question, you don't actually expect to have someone reply (you might even be alone), but you are expressing your frustration for your inability to find whatever you are looking for.
2-"Chi sa..." is "does anybody know...?" This is an actual question. "Chi sa dov'è?" You are actually asking a group of people if they know where the thing is.
I haven't said they are interchangeable, but "chissà" means exactly "chi sa", because it comes from that.
"Chissà/Chi sa dove l'hanno messa!" are the same. Using subjunctive is wrong in any case.
Also you use the indicative for yourself in the second point ("Chi sa dov'è?"). "Chi sa dove l'hanno messa?" is the right form. You don't need subjunctive.
Of course "chissà" comes from "chi sa" but its meaning has slightly shifted so it is not anymore pronoun+verb.
Definitely "Chissà dove l'hanno messa!" is the form I would use and I would find "Chi sa dove l'hanno messa!" questionable at best. You use "chi sa" when you are making an actual question (Chi sa dove l'hanno messa?), and in this case "chissà" would be wrong
Also I don't understand, you are saying that "Chi sa dov'è?" is incorrect?
Source: native speaker