I'm away from my books right now, but if I were home Olga's Alexandrovna's memoirs are the first place I'd check. I'm 99% sure she mentions schwipsig/shvybzik, but I can't recall whether she uses "imp."
Personally, I suspect there is no source for "imp." I don't think it was ever used by the family. Somewhere along the line the mistaken (but very prevalent) notion developed that shvybzik is Russian for imp, and Anastasia gained a retrospective nickname among English-speakers.
Thank you, "Sharushka," for weighing in on "Georgiy"'s question re the origin of the alleged nickname of the GD Anastasia N. as "Imp." I remember that this has come up several times over the years. I have always treated the appellation with disdain, being IMO, a cutesy-cutesy pseudo-affectionate tag created out of English analogy and thin air, and perpetuated by would-be writers/commentators who desperately want to demonstrate that they were/are privy to affectionate Romanov family/personal nicknames.
I, like you, feel VERY certain indeed that the GD Olga A. employed, and may even have given the name "Schwipsig/shvybzik" to the GD Anastasia N. The excellent Greg King/Penny Wilson's book, "The Resurrection of the Romanovs" has a chapter (2) entitled "The Imp", but nowhere do I find reference to the origin (of "Imp", per se), RATHER they DO devote space to the name"Schwibzik/Schwibes" on pps 121,127-128. Therefore, as you say: "I suspect there is no source for "imp." I don't think that it was ever used by the family."
Somewhere, I have a vague recollection (but I cannot document it at the moment) that the "tipsy" occurred in reference to an incident wherein the GD Anastasia N. turned over or fell from a chair in which she was sitting. To use such an intimate description certainly portends that it was a family member who had knowledge of German to transpose or transliterate the word. I have NEVER seen an authenticated, documented reference from one of the family members writing in letters, being authoritatively quoted, etc. as to the child being addressed as "Imp." Should someone have such documentation as described, now is the time to cite your references. Regards, AP.