Does "shot of espresso" translate into Italian as "colpo di caffé espresso", or is there a different way of saying this, such as tazza?
As a native Italian speaker, I've never encountered the expression "colpo di caffè espresso" (please notice the Italian word is "caffè", with a double "f"). In general, we do not even specify "espresso" and simply say "un caffè" ("espresso" is implied, and we have to specify only if we do not want an espresso). For what concerns the "shot", we use that term (in English) in reference to super alcoholic drinks but not for coffee. In conclusion, I'd translate "shot of espresso" with "caffè ristretto"
While I agree the word "caffettino" (as suggested by @ZabZonk) is informal, I'd say it is used as term of endearment rather than as diminutive and it suggests the idea of "well deserved" and/or "enjoyable" rather than "small".