Don't tell him, Pike!
Reverting to sensible answers (for the time being), it depends on how "late" your "late Italian Wars" army is. I'm not sure what rules/army lists you are using, but my Field of Glory: Renaissance lists (Vol. 1 - Trade & Treachery) has this to say on the subject of Italian Wars pike:-
"Pike-armed Florentine militia are first mentioned in 1506 when 10,000 trained by professional soldiers were fielded, although Machiavelli mentions in a letter that 12,000 were present, and 20,000 may have been planned. They may have ceased to exist after 1512 when the Medici were restored to power.... They are described as being issued with a pike and harness (ie body armour) and a uniform of a white jerkin and hose with one leg red and the other white.....With the exception of Florence, and to a lesser extent the Papacy, Italian infantry rarely used the pike, and even when they did they were in such small numbers that they do not justify representation by a battle group."
In the "Italian States" army list - which covers the period from 1494 until all states other than Venice ceased to field independent armies - the only pike listed are as "Landsknechts or other mercenaries" and are limited to units of 10-16 bases (up to 2 of which can be "heavy weapon" - ie halberd or two-handed sword), and only 24 bases maximum, so you could have at most, say, 2 units, each of 12 bases, either all pike, or 10 pike and 2 heavy weapons. A separate Papal list allows for similar numbers of bases of Romagnol pike for most of this period, whilst an "early" Venetian list only allows "Romagnol, Landsknecht or other mercenary" pike, but notes that these only appear sporadically after their defeat at Agnadello in 1509 (the "early" Venetian list runs up to 1550; the "late" Venetian list allows Landsknecht pike up to 1601, and optional militia pike - the latter only classified as "poor" - up to 1581).
Not sure if that helps you very much (especially if you are using a different rule set!), but I would say that all pike in a Milanese army, for the period you are working with, would most likely be Landsknechts.
BvW