Why does the Torah switch the word for men from כְלִי to שִׂמְלַת for women?
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The Malbi"m there brings down a dispute over the meanings of the two terms. Either כלי and שמלה are synonyms and both refer to articles of clothing, or כלי is a broader term that includes clothing (such as שמלות) and other things. He brings extensive proofs for the opinion that differentiates between the two.*
The phrases in which the two words are found are actually quite different. One is
and the other is
The verb in the latter phrase is semantically much broader in that it refers merely to "being upon" a person, rather than specifically wearing, which indicates that the object of the verb, "instrument," as opposed to "garment," could also be more general. Additionally the term for "garment" in this case is even more specific than the more common term for garment (applied to this exact set of prohibitions by חז"ל), i.e. בגד. Instead the Torah uses שמלה, which was used recently in the phrase שמלת שביה, contextually associated with an object of beautification. Finally כלי גבר is lexically associated with כלי גבור מלחמה ~ the instruments of a warrior.
All of this is to argue that a man is prohibited from wearing (specifically provocative) clothing of a woman, whereas a woman is prohibited from putting on (specifically war-like) items that would normally be used only by men.
*I would point out that לפע"ד, the second opinion could come לבאר ולא לחלק, but there is no harm in separating them.
Rav Chaim Kanievsky answers that the Torah is including weapons or כְלִי of war and hence to include the Issur it changed the wording to make it gender Specific.
The sefer Ohel Moshe here brings the following explanation of R. Nosson Adler:
Translation taken from here.