Piccolo means small in Italian.
If you just mean small just say "small". If by Piccolo (with a capital P) you mean some made up version of coffee.... I will have you know that in Italy they have never heard of it and therefore it is utter bullshit.
The problem my dear flightless bird, is that to keep their voracious landlords and shareholders happy, they have to turn a simple, delicious beverage in an ordeal, so that they can charge extortionate prices to the hordes of morons that keep their pockets lined.
In Italy (except in the few places already corrupted by this hipster BS) you can only order three basic types of coffee-based beverages: an espresso, a macchiato and a cappuccino.
Lattes, flat whites, double-shots, almond milk, extra hot, and a thousand other variants are simply abhorrent.
Moreover, these drinks have defaults. If you just enter a bar and ask for - caffe' -, within 30 seconds you will be presented with a well made espresso. No questions asked.
You just had to utter one word.
Try entering a Costa and saying "coffee" and see what happens.
Each one of three drinks comes only in one size. The right size.
Espresso and macchiato use the same small cup, and the cappuccino is smaller than a small cappuccino in London.
A latte is not a thing. Latte just means milk.
There is something called a caffellatte, which is a milky coffee that you are only allowed to drink for breakfast if you are 8 years old or younger.
You can ask for an espresso "corto" or "lungo" but it's rather exceptional and all they do is to run the machine a few seconds shorter or longer. Same cup and everything.
The macchiato and cappuccino only come with full fat milk, the right milk, and the only one that can make a silky smooth froth.
If you want something with another type of milk, you can ask.. but a lot of places will look at you funny for wasting their time, most of the time they will refuse to make it and they will tell you that what you are asking is wrong and you are therefore welcome to make it at your own home.
Decaffeinated is an option but quite rare as - like any Italian will tell you - it defeats the purpose and tastes like shit.
Every Italian I know wonders why you had to take something perfectly fine, simple, and delicious, and wholly ruin it.
And to add insult to injury, doing so using Italian words. Couldn't you at least own to it, and ruin stuff in your own words?
P.S. In the US, of course there also used to be a default, a coffee was just a medium size 'drip' coffee. Which is perfectly fine as a default for another continent, as it is also one single option and zero BS - and therefore approved.