I'm going to extend Perry Webb's answer of YES (the grammar allows it) and the JPS background context of Zech 13:2-6 that it is about false prophets trying to hide their previous activities of being false prophets.
Zech 13:4 can be read that the false prophets are afraid of being killed (v 3) so they no longer want to wear the prophetic office's usual attire of hairy cloak which they used to wear when they were still deceiving the people by delivering messages that didn't come from the LORD.
The following are quotes from the 2008 New American Commentary on Zechariah by George Klein to support the above reading as well as to explain vv. 5-6 about the wounds:
13:4: ...
In the coming age the false prophets will be ashamed of their deeds in misrepresenting the righteous Lord and in misleading God's people. ...
These false prophets will be ashamed of their prior “prophetic visions.” This shame reflects their deep desire that their evil actions remain hidden,⁵⁰³ but the false prophets' response does not constitute a repentant attitude. ... These prophets' willingness to lie about their prior misdeeds (vv. 5–6) manifests their deepest intentions in removing their prophetic robes. Eschewing their days of glory, they exchanged their prophetic mantles that had symbolized their fame, in the hopes of fading into obscurity and thus avoiding the punishment they so deserved.
In an attempt to escape the death penalty, these frauds would cease clothing themselves with the “garment of hair” (’addereṯ śê‘ār), the attire that publicly set prophets apart [like John the Baptist who clothed himself in a mantle of camel hair]. ...
13:5-6 Verse 4 reveals the false prophets' attempt to conceal their past actions by removing the official attire of the prophetic office. In vv. 5–6 they continue their charade with the verbal equivalent of taking off their prophetic mantles, the disavowal that they ever served in a prophetic role. Whenever it will better serve their personal interests, a common theme in Zechariah's excoriation of false prophets, they would not hesitate to lie. These evil men will seek to hide among the humblest individuals in society by pretending to be something they are not, a role they have had great experience in playing.⁵⁰⁹
The false prophets adopted traditional prophetic language to deny their prior activities, drawing from the language of Amos, who told Amaziah, priest at Bethel, “I was neither a prophet nor a prophet's son, but I was a shepherd, and I also took care of sycamore-fig trees” (7:14). Amos meant that when God called him he was neither already a prophet (nabî) nor the “son of a prophet” (ben-nabî), the latter commonly understood to mean that he did not belong to a prophetic guild.⁵¹⁰
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... Clothed with the attire of common laborers, the false prophets find it difficult to obscure their former activities. Perhaps when the charlatans stripped to work in the fields the wounds that testified to their prophetic activities condemned them. The accusatory question, “What are these wounds on your body?” sought to disclose the prophets' true identity. This question holds the potential both to reveal the imposters as false prophets and to catch them in an outright lie. The connection between physical injuries or scars and false prophets requires examination.
Zechariah's expression “wounds on your body” merits scrutiny. The word “wounds” (hammakkôt) is a general term for “injuries” (1 Kgs 22:35; Isa 1:6).⁵²³ Canaanite religious rites included various expressions of self mutilation. The clearest biblical example of these practices appears in the contest between Elijah and the prophets of Baal on Mount Carmel (1 Kgs 18). At the height of the religious frenzy, the Baal worshippers “shouted louder and slashed themselves with swords and spears, as was their custom, until the blood flowed” (1 Kgs 18:28). Leviticus 19:28 and Deut 14:1 explicitly forbid any such behavior by the divine rationale, “I am the LORD.” The Mount Carmel episode suggests that the fervent self wounding hoped to impress the deity with the worshipper's devotion and to move the god to act as requested. The pagan background to Zech 13:6 suggests that self mutilation characterized false prophets. Thus, when these wounds would become visible to their neighbors, the false prophets could hide their true identity no longer.⁵²⁴
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The charlatans' feeble reply contends that the false prophets had received their wounds “at the house of my friends.” ...